OMG UML2.0 OCL specification

Transcription

UML 2.0 OCL Specification
This OMG document replaces the submission document (ad/03-01-07) and the Draft Adopted
specification (ptc/03-08-08). It is an OMG Final Adopted Specification and is currently in the
finalization phase. Comments on the content of this document are welcomed, and should be
directed to issues@omg.org by November 15, 2003.
You may view the pending issues for this specification from the OMG revision issues web page
http://www.omg.org/issues/.
The FTF Recommendation and Report for this specification will be published on April 30, 2004. If
you are reading this after that date, please download the available specification from the OMG
Specifications Catalog.
NOTE: Appendix A - Semantics is the original submission document due to the numerous
equations used throughout the document.
OMG Adopted Specification
ptc/03-10-14
Date: October 2003
OCL 2.0
OMG Final Adopted Specification
ptc/03-10-14
Copyright © 2001-2003 Adaptive Ltd.
Copyright © 2001-2003 Boldsoft
Copyright © 2001-2003 International Business Machines Corporation
Copyright © 2001-2003 IONA Technologies
Copyright © 1997-2003 Object Management Group.
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Table of Contents
1
2
3
4
5
6
Scope ............................................................................................. 1
Conformance .................................................................................. 1
Normative References .................................................................... 2
Terms and Definitions ..................................................................... 2
Symbols .......................................................................................... 2
Additional Information ..................................................................... 2
6.1 Changes to Adopted OMG Specifications ........................................................... 2
6.2 Structure of the specification ............................................................................... 2
6.3 Acknowledgements ............................................................................................. 3
7 OCL Language Description ............................................................ 5
7.1 Why OCL? ........................................................................................................... 5
7.1.1 Where to Use OCL.................................................................................................. 5
7.2 Introduction ......................................................................................................... 6
7.2.1 Legend .................................................................................................................... 6
7.2.2 Example Class Diagram .......................................................................................... 6
7.3 Relation to the UML Metamodel .......................................................................... 7
7.3.1 Self .......................................................................................................................... 7
7.3.2 Specifying the UML context .................................................................................... 7
7.3.3 Invariants ................................................................................................................ 8
7.3.4 Pre- and Postconditions .......................................................................................... 8
7.3.5 Package Context..................................................................................................... 9
7.3.6 Operation Body Expression .................................................................................... 9
7.3.7 Initial and Derived Values ....................................................................................... 9
7.3.8 Other Types of Expressions .................................................................................. 10
7.4 Basic Values and Types .................................................................................... 10
7.4.1 Types from the UML Model ................................................................................... 11
7.4.2 Enumeration Types ............................................................................................... 11
7.4.3 Let Expressions ..................................................................................................... 11
7.4.4 Additional operations/attributes through «definition» expressions ........................ 11
7.4.5 Type Conformance ................................................................................................ 12
7.4.6 Re-typing or Casting ............................................................................................. 13
7.4.7 Precedence Rules ................................................................................................. 13
7.4.8 Use of Infix Operators ........................................................................................... 14
7.4.9 Keywords .............................................................................................................. 14
7.4.10 Comment ............................................................................................................. 14
7.5 Objects and Properties ...................................................................................... 15
7.5.1 Properties: Attributes ............................................................................................. 15
7.5.2 Properties: Operations .......................................................................................... 16
7.5.3 Properties: AssociationEnds and Navigation ....................................................... 17
OCL Adopted Specification
i
7.5.4 Navigation to Association Classes ........................................................................ 18
7.5.5 Navigation from Association Classes .................................................................... 19
7.5.6 Navigation through Qualified Associations ............................................................ 20
7.5.7 Using Pathnames for Packages ............................................................................ 20
7.5.8 Accessing overridden properties of supertypes .................................................... 20
7.5.9 Predefined properties on All Objects ..................................................................... 21
7.5.10 Features on Classes Themselves ....................................................................... 22
7.5.11 Collections ........................................................................................................... 22
7.5.12 Collections of Collections .................................................................................... 23
7.5.13 Collection Type Hierarchy and Type Conformance Rules .................................. 23
7.5.14 Previous Values in Postconditions ...................................................................... 24
7.5.15 Tuples ................................................................................................................. 25
7.6 Collection Operations ........................................................................................ 25
7.6.1 Select and Reject Operations ............................................................................... 25
7.6.2 Collect Operation .................................................................................................. 27
7.6.3 ForAll Operation .................................................................................................... 28
7.6.4 Exists Operation .................................................................................................... 28
7.6.5 Iterate Operation ................................................................................................... 29
7.7 Messages in OCL .............................................................................................. 29
7.7.1 Calling operations and sending signals ................................................................. 29
7.7.2 Accessing result values ......................................................................................... 30
7.7.3 An example ........................................................................................................... 31
7.8 Resolving Properties ......................................................................................... 32
8 Abstract Syntax ............................................................................ 33
8.1 Introduction ........................................................................................................ 33
8.2 The Types Package .......................................................................................... 33
8.2.1 Type Conformance ................................................................................................ 35
8.2.2 Well-formedness Rules for the Types Package .................................................... 38
8.3 The Expressions Package ................................................................................. 40
8.3.1 Expressions Core.................................................................................................. 40
8.3.2 Model PropertyCall Expressions ........................................................................... 44
8.3.3 If Expressions ........................................................................................................ 46
8.3.4 Message Expressions ........................................................................................... 46
8.3.5 Literal Expressions ................................................................................................ 48
8.3.6 Let expressions ..................................................................................................... 50
8.3.7 Well-formedness Rules of the Expressions package ............................................ 51
8.3.8 Additional Operations on UML metaclasses ......................................................... 56
8.3.9 Additional Operations on OCL metaclasses ......................................................... 58
8.3.10 Overview of class hierarchy of OCL Abstract Syntax metamodel ....................... 60
9 Concrete Syntax ........................................................................... 61
9.1 Structure of the Concrete Syntax ...................................................................... 61
9.2 A Note to Tool Builders ..................................................................................... 63
9.2.1 Parsing .................................................................................................................. 63
9.2.2 Visibility ................................................................................................................. 63
9.3 Concrete Syntax ................................................................................................ 63
9.3.1 Comments ............................................................................................................. 89
9.3.2 Operator Precedence ............................................................................................ 89
9.4 Environment definition ....................................................................................... 89
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9.4.1 Environment .......................................................................................................... 89
9.4.2 NamedElement ..................................................................................................... 91
9.4.3 Namespace ........................................................................................................... 92
9.5 Concrete to Abstract Syntax Mapping ............................................................... 92
9.6 Abstract Syntax to Concrete Syntax Mapping ................................................... 92
10Semantics Described using UML ................................................. 93
10.1 Introduction ..................................................................................................... 93
10.2 The Values Package ....................................................................................... 94
10.2.1 Definitions of concepts for the Values package ................................................... 95
10.2.2 Well-formedness rules for the Values Package .................................................. 99
10.2.3 Additional operations for the Values Package .................................................. 100
10.2.4 Overview of the Values package ....................................................................... 101
10.3 The Evaluations Package ............................................................................. 102
10.3.1 Definitions of concepts for the Evaluations package ......................................... 103
10.3.2 Model PropertyCall Evaluations ........................................................................ 106
10.3.3 If Expression Evaluations .................................................................................. 107
10.3.4 Ocl Message Expression Evaluations ............................................................... 108
10.3.5 Literal Expression Evaluations .......................................................................... 109
10.3.6 Let expressions ................................................................................................. 111
10.3.7 Well-formedness Rules of the Evaluations package ......................................... 112
10.3.8 Overview of the Values package ....................................................................... 119
10.4 The AS-Domain-Mapping Package ............................................................... 120
10.4.1 Well-formedness rules for the AS-Domain-Mapping.type-value Package ........ 123
10.4.2 Additional operations for the AS-Domain-Mapping.type-value Package .......... 124
10.4.3 Well-formedness rules for the AS-Domain-Mapping.exp-eval Package ........... 124
11The OCL Standard Library ......................................................... 131
11.1 Introduction ................................................................................................... 131
11.2 The OclAny, OclVoid, and OclMessage types .............................................. 131
11.2.1 OclAny .............................................................................................................. 131
11.2.2 OclMessage ...................................................................................................... 132
11.2.3 OclVoid ............................................................................................................. 133
11.2.4 Operations and well-formedness rules .............................................................. 133
11.2.5 OclMessage ...................................................................................................... 134
11.2.6 OclVoid ............................................................................................................. 134
11.3 ModelElement types ...................................................................................... 134
11.3.1 OclModelElement .............................................................................................. 135
11.3.2 OclType ............................................................................................................. 135
11.3.3 OclState ............................................................................................................ 135
11.3.4 Operations and well-formedness rules .............................................................. 135
11.4 Primitive Types .............................................................................................. 136
11.4.1 Real ................................................................................................................... 136
11.4.2 Integer ............................................................................................................... 136
11.4.3 String ................................................................................................................. 136
11.4.4 Boolean ............................................................................................................. 136
11.5 Operations and well-formedness rules .......................................................... 136
11.5.1 Real ................................................................................................................... 136
11.5.2 Integer ............................................................................................................... 137
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11.5.3 String ................................................................................................................. 138
11.5.4 Boolean ............................................................................................................. 139
11.6 Collection-Related Types .............................................................................. 139
11.6.1 Collection .......................................................................................................... 140
11.6.2 Set ..................................................................................................................... 140
11.6.3 OrderedSet ........................................................................................................ 140
11.6.4 Bag .................................................................................................................... 140
11.6.5 Sequence .......................................................................................................... 140
11.7 Operations and well-formedness rules .......................................................... 140
11.7.1 Collection .......................................................................................................... 140
11.7.2 Set ..................................................................................................................... 141
11.7.3 OrderedSet ........................................................................................................ 143
11.7.4 Bag .................................................................................................................... 144
11.7.5 Sequence .......................................................................................................... 146
11.8 Predefined Iterator Expressions .................................................................... 149
11.8.1 Extending the standard library with iterator expressions ................................... 149
11.9 Mapping rules for predefined iterator expressions ........................................ 149
11.9.1 Collection .......................................................................................................... 149
11.9.2 Set ..................................................................................................................... 150
11.9.3 Bag .................................................................................................................... 151
11.9.4 Sequence .......................................................................................................... 152
12The Use of Ocl Expressions in UML Models .............................. 155
12.1 Introduction .................................................................................................... 155
12.1.1 UML 2.0 Alignment ............................................................................................ 155
12.2 The ExpressionInOcl Type ............................................................................ 155
12.2.1 ExpressionInOcl ................................................................................................ 156
12.3 Well-formedness rules ................................................................................... 156
12.3.1 ExpressionInOcl ................................................................................................ 156
12.4 Standard placements of OCL Expressions ................................................... 157
12.4.1 How to extend the use of OCL at other places ................................................. 157
12.5 Definition ....................................................................................................... 157
12.5.1 Well-formedness rules ...................................................................................... 157
12.6 Invariant ......................................................................................................... 158
12.7 Precondition .................................................................................................. 158
12.8 Postcondition ................................................................................................. 159
12.9 Initial value expression .................................................................................. 160
12.10 Derived value expression ............................................................................ 161
12.11 Operation body expression ......................................................................... 161
12.12 Guard .......................................................................................................... 162
12.12.1 Well-formedness rules .................................................................................... 162
12.13 Concrete Syntax of Context Declarations ................................................... 163
12.13.1 packageDeclarationCS ................................................................................... 163
12.13.2 contextDeclarationCS ..................................................................................... 163
12.13.3 attrOrAssocContextCS .................................................................................... 164
iv
12.13.4 initOrDerValueCS ............................................................................................ 164
12.13.5 classifierContextDeclCS .................................................................................. 164
12.13.6 invOrDefCS ..................................................................................................... 164
12.13.7 defExpressionCS ............................................................................................ 164
12.13.8 operationContextDeclCS ................................................................................. 164
12.13.9 prePostOrBodyDeclCS ................................................................................... 165
12.13.10 operationCS .................................................................................................. 165
12.13.11 parametersCS ............................................................................................... 165
13Alignment of OCL, UML and MOF Metamodels ........................ 167
13.1
13.2
13.3
13.4
Introduction ................................................................................................... 167
Use of the UML Metamodel .......................................................................... 167
Use of the OCL metamodel in the UML metamodel ..................................... 168
Wishlist .......................................................................................................... 169
Appendix A - Semantics ..................................................................A-1
Appendix B - Interchange Format ....................................................B-1
Index ..................................................................................................... Index-1
v
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List of Figures
Class Diagram Example 7
Navigating recursive association classes 19
Accessing Overridden Properties Example 21
OclMessage Example 31
Abstract syntax kernel metamodel for OCL Types 34
The basic structure of the abstract syntax kernel metamodel for Expressions 40
Abstract syntax metamodel for ModelPropertyCallExp in the Expressions package 44
Abstract syntax metamodel for if expression 46
The abstract syntax of Ocl messages 47
Abstract syntax metamodel for Literal expression 49
Abstract syntax metamodel for let expression 51
Overview of the abstract syntax metamodel for Expressions 60
The Environment type 62
Overview of packages in the UML-based semantics 94
The kernel values in the semantic domain 95
The collection and tuple values in the semantic domain 96
The message values in the semantic domain 98
The inheritance tree of classes in the Values package 102
The environment for ocl evaluations 103
Domain model for ocl evaluations
104
Domain model for ModelPropertyCallExpEval and subtypes
106
Domain model for if expression 108
Domain model for message evaluation 109
Domain model for literal expressions 110
Domain model for let expression 111
The inheritance tree of classes in the Evaluations package 120
Associations between values and the types defined in the abstract syntax. 121
The types defined in the OCL standard library 132
Metaclass ExpressionInOcl added to the UML metamodel 156
Situation of Ocl expression used as definition or invariant 157
An OCL ExpressionInOcl used as a pre- or post-condition. 159
Expression used to define the inital value of an attribute 161
An OCL expression used as a Guard expression 162
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List of Tables
Overview of OCL compliance points 1
Basic Types 10
Operations on predefined types 10
Type conformance rules 12
Valid Expressions 13
Overview of UML 1.4 metaclasses used in this submission 167
Overview of places in a model where an OCL expression may be used 168
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1
Scope
This specification contains defines the Object Constraint Language (OCL), version 2.0. OCL version 2.0 is the version of
OCL that is aligned with UML 2.0 and MOF 2.0.
2
Conformance
The UML 2.0 Infrastructure and the MOF 2.0 Core submissions that are being developed in parallel with this OCL 2.0
submission share a common core. The OCL specification contains a well-defined and named subset of OCL that is
defined purely based on the common core of UML and MOF. This allows this subset of OCL to be used with both the
MOF and the UML, while the full specification can be used with the UML only.
The following compliance points are distinguished for both parts.
1.
Syntax compliance. The tool can read and write OCL expressions in accordance with the grammar, including validating its type conformance and conformance of well-formedness rules against a model.
2.
XMI compliance. The tool can exchage OCL expressions using XMI.
3.
Evaluation compliance. The tool evaluates OCL expressions in accordance with the semantics chapter. The following
additional compliance points are optional for OCL evaluators, as they are dependent on the technical platform on
which they are evaluated.
• allInstances()
• pre-values and oclIsNew() in postconditions
• OclMessage
• navigating across non-navigable associations
• accessing private and protected features of an object
The following table shows the possible compliance points. Each tools is expected to fill in this table to specify which
compliance point are supported.
Table 1. Overview of OCL compliance points
OCL-MOF subset
Full OCL
Syntax
XMI
Evaluation
- allInstances
- @pre in postcondtions
- OclMessage
- navigating non-navigable associations
- accessing proivate and protected features
UML OCL 2.0 Adopted Specification
1
3
Normative References
The following normative documents contain provisions which, through reference in this text, constitute provisions of this
specification. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply.
• UML 2.0 Superstructure Specification
• UML 2.0 Infrastructure Specification
• MOF 2.0 Core Specification
4
Terms and Definitions
For the purposes of this specification, the terms and definitions given in the normative references and the following apply.
Editorial Comment: Needs to be completed (or possibly eliminated).
5
.Symbols
List of symbols/abbreviations.
Editorial Comment: Needs to be completed (or possibly eliminated).
6
Additional Information
6.1
Changes to Adopted OMG Specifications
This specification replaces the specification of OCL given in UML 1.4.1 and UML 1.5.
6.2
Structure of the specification
The document is divided into several chapters.
The OCL Language Description chapter gives an informal description of OCL in the style that has been used in the UML
1.1 through 1.4. This section is not normative, but meant to be explanatory.
Chapter 8 (“Abstract Syntax”) describes the abstract syntax of OCL using a MOF 2.0 compliant metamodel. This is the
same approach as used in the UML 1.4 and other UML 2.0 submissions. The metamodel is MOF 2.0 compliant in the
sense that it only uses constructs that are defined in the MOF 2.0.
Chapter 9 (“Concrete Syntax”) describes the canonical concrete syntax using an attributed EBNF grammar. This syntax is
mapped onto the abstract syntax, achieving a complete separation between concrete and abstract syntax.
Chapter 10 (“Semantics Described using UML”) describes the semantics for OCL using UML.
2
In section 11 (“The OCL Standard Library”) the OCL Standard Library is described. This defines type like Integer,
Boolean, etc. and all the collection types. OCL is not a stand-alone language, but an integral part of the UML. An OCL
expression needs to be placed within the context of a UML model.
Section 12 (“The Use of Ocl Expressions in UML Models”) describes a number of places within the UML where OCL
expressions can be used.
Appendix A (“Semantics”) describes the underlying semantics of OCL using a mathematical formalism. This appendix,
however is not normative, but ment for the readers that need a mathematical description for the semantics of OCL.
Appendix B (“Interchange Format”) is currently a place holder for an interchange format, which can be defined along the
same lines as XMI.
6.3
Acknowledgements
The following companies submitted and/or supported parts of this specification:
• BoldSoft
• Dresden University of Technology
• Kings College
• Klasse Objecten
• Rational Software Corporation
• Borland Software Corporation
• University of Bremen
• IONA
• Adaptive Ltd
• International Business Machines
• Telelogic
• Kabira Technologies Inc.
• University of Kent
• Project Technology Inc.
• University of York
• Compuware Corporation
• Syntropy Ltd.
• Oracle
• Softeam
3
4
7
OCL Language Description
This chapter introduces the Object Constraint Language (OCL), a formal language used to describe expressions on UML
models. These expressions typically specify invariant conditions that must hold for the system being modeled or queries
over objects described in a model. Note that when the OCL expressions are evaluated, they do not have side effects; i.e.
their evaluation cannot alter the state of the corresponding executing system.
OCL expressions can be used to specify operations / actions that, when executed, do alter the state of the system. UML
modelers can use OCL to specify application-specific constraints in their models. UML modelers can also use OCL to
specify queries on the UML model, which are completely programming language independent.
This chapter is informative only and not normative.
7.1
Why OCL?
A UML diagram, such as a class diagram, is typically not refined enough to provide all the relevant aspects of a
specification. There is, among other things, a need to describe additional constraints about the objects in the model. Such
constraints are often described in natural language. Practice has shown that this will always result in ambiguities. In order
to write unambiguous constraints, so-called formal languages have been developed. The disadvantage of traditional
formal languages is that they are usable to persons with a strong mathematical background, but difficult for the average
business or system modeler to use.
OCL has been developed to fill this gap. It is a formal language that remains easy to read and write. It has been developed
as a business modeling language within the IBM Insurance division, and has its roots in the Syntropy method.
OCL is a pure specification language; therefore, an OCL expression is guaranteed to be without side effect. When an
OCL expression is evaluated, it simply returns a value. It cannot change anything in the model. This means that the state
of the system will never change because of the evaluation of an OCL expression, even though an OCL expression can be
used to specify a state change (e.g., in a post-condition).
OCL is not a programming language; therefore, it is not possible to write program logic or flow control in OCL. You
cannot invoke processes or activate non-query operations within OCL. Because OCL is a modeling language in the first
place, OCl expressions are not by definition directly executable.
OCL is a typed language, so that each OCL expression has a type. To be well formed, an OCL expression must conform
to the type conformance rules of the language. For example, you cannot compare an Integer with a String. Each Classifier
defined within a UML model represents a distinct OCL type. In addition, OCL includes a set of supplementary predefined
types. These are described in Chapter 11 (“The OCL Standard Library”).
As a specification language, all implementation issues are out of scope and cannot be expressed in OCL.
The evaluation of an OCL expression is instantaneous. This means that the states of objects in a model cannot change
during evaluation.
7.1.1
Where to Use OCL
OCL can be used for a number of different purposes:
• As a query language
• To specify invariants on classes and types in the class model
5
• To specify type invariant for Stereotypes
• To describe pre- and post conditions on Operations and Methods
• To describe Guards
• To specify target (sets) for messages and actions
• To specify constraints on operations
• To specify derivation rules for attributes for any expression over a UML model.
7.2
Introduction
7.2.1
Legend
Text written in the Letter Gothic typeface as shown below is an OCL expression.
'This is an OCL expression'
The context keyword introduces the context for the expression. The keyword inv, pre and post denote the stereotypes,
respectively «invariant», «precondition», and «postcondition», of the constraint. The actual OCL expression comes after
the colon.
context TypeName inv:
'this is an OCL expression with stereotype <<invariant>> in the
context of TypeName' = 'another string'
In the examples the keywords of OCL are written in boldface in this document. The boldface has no formal meaning, but
is used to make the expressions more readable in this document. OCL expressions are written using ASCII characters
only.
Words in Italics within the main text of the paragraphs refer to parts of OCL expressions.
7.2.2
Example Class Diagram
The diagram below is used in the examples in this chapter.
6
«enumeration»
Gender
Bank
male
female
accountNumber:Integer
0..1
0..* customer
Person
isMarried : Boolean
isUnemployed : Boolean
birthDate : Date
age : Integer
firstName : String
lastName : String
gender : Gender
income(Date) : Integer
0..*
manager
1
managedCompanies
employee
0..*
wife
0..1
husband 0..1
employer
0..*
Company
name : String
numberOfEmployees : Integer
stockPrice() : Real
Job
title : String
startDate : Date
salary : Integer
Marriage
place : String
date : Date
Figure 1 - Class Diagram Example
7.3
Relation to the UML Metamodel
7.3.1
Self
Each OCL expression is written in the context of an instance of a specific type. In an OCL expression, the reserved word
self is used to refer to the contextual instance. For instance, if the context is Company, then self refers to an instance of
Company.
7.3.2
Specifying the UML context
The context of an OCL expression within a UML model can be specified through a so-called context declaration at the
beginning of an OCL expression. The context declaration of the constraints in the following sections is shown.
7
If the constraint is shown in a diagram, with the proper stereotype and the dashed lines to connect it to its contextual
element, there is no need for an explicit context declaration in the test of the constraint. The context declaration is
optional.
7.3.3
Invariants
The OCL expression can be part of an Invariant which is a Constraint stereotyped as an «invariant». When the invariant
is associated with a Classifier, the latter is referred to as a “type” in this chapter. An OCL expression is an invariant of the
type and must be true for all instances of that type at any time. (Note that all OCL expressions that express invariants are
of the type Boolean.)
For example, if in the context of the Company type in Figure 1 on page 7, the following expression would specify an
invariant that the number of employees must always exceed 50:
self.numberOfEmployees > 50
where self is an instance of type Company. (We can view self as the object from where we start evaluating the
expression.) This invariant holds for every instance of the Company type.
The type of the contextual instance of an OCL expression, which is part of an invariant, is written with the context
keyword, followed by the name of the type as follows. The label inv: declares the constraint to be an «invariant»
constraint.
context Company inv:
self.numberOfEmployees > 50
In most cases, the keyword self can be dropped because the context is clear, as in the above examples. As an alternative
for self, a different name can be defined playing the part of self:
context c : Company inv:
c.numberOfEmployees > 50
This invariant is equivalent to the previous one.
Optionally, the name of the constraint may be written after the inv keyword, allowing the constraint to be referenced by
name. In the following example the name of the constraint is enoughEmployees. In the UML 1.4 metamodel, this name is
a (meta-)attribute of the metaclass Constraint that is inherited from ModelElement.
context c : Company inv enoughEmployees:
c.numberOfEmployees > 50
7.3.4
Pre- and Postconditions
The OCL expression can be part of a Precondition or Postcondition, corresponding to «precondition» and «postcondition»
stereotypes of Constraint associated with an Operation or other behavioral feature. The contextual instance self then is an
instance of the type which owns the operation or method as a feature. The context declaration in OCL uses the context
keyword, followed by the type and operation declaration. The stereotype of constraint is shown by putting the labels
‘pre:’ and ‘post:’ before the actual Preconditions and Postconditions
context Typename::operationName(param1 : Type1, ... ): ReturnType
pre : param1 > ...
post: result = ...
8
The name self can be used in the expression referring to the object on which the operation was called. The reserved word
result denotes the result of the operation, if there is one. The names of the parameters (param1) can also be used in the
OCL expression. In the example diagram, we can write:
context Person::income(d : Date) : Integer
post: result = 5000
Optionally, the name of the precondition or postcondition may be written after the pre or post keyword, allowing the
constraint to be referenced by name. In the following example the name of the precondition is parameterOk and the name
of the postcondition is resultOk. In the UML metamodel, these names are the values of the attribute name of the
metaclass Constraint that is inherited from ModelElement.
pre parameterOk: param1 > ...
post resultOk : result = ...
7.3.5
Package Context
The above context declaration is precise enough when the package in which the Classifier belongs is clear from the
environment. To specify explicitly in which package invariant, pre or postcondition Constraints belong, these constraints
can be enclosed between 'package' and 'endpackage' statements. The package statements have the syntax:
package Package::SubPackage
context X inv:
... some invariant ...
context X::operationName(..)
pre: ... some precondition ...
endpackage
An OCL file (or stream) may contain any number package statements, thus allowing all invariant, preconditions and
postconditions to be written and stored in one file. This file may co-exist with a UML model as a separate entity.
7.3.6
Operation Body Expression
An OCL expression may be used to indicate the result of a query operation. This can be done using the following syntax:
body: -- some expression
The expression must conform to the result type of the operation. Like in the pre- and postconditions, the parameters may
be used in the expression. Pre-, and postconditions, and body expressions may be mixed together after one operation
context. For example:
context Person::getCurrentSpouse() : Person
pre: self.isMarried = true
body: self.mariages->select( m | m.ended = false ).spouse
7.3.7
Initial and Derived Values
An OCL expression may be used to indicate the initial or derived value of an attribute or association end. This can be
done using the following syntax:
9
context Typename::attributeName: Type
init: -- some expression representing the initial value
context Typename::assocRoleName: Type
derive: -- some expression representing the derivation rule
The expression must conform to the result type of the attribute. In the case the context is an association end the
expression must conform to the classifier at that end when the multiplicity is at most one, or Set or OrderedSet when the
multiplicity may be more than one. Initial, and derivation expressions may be mixed together after one context. For
example:
context Person::income : Integer
init: parents.income->sum() * 1% -- pocket allowance
derive: if underAge
then parents.income->sum() * 1% -- pocket allowance
else job.salary
-- income from regular job
endif
7.3.8
Other Types of Expressions
Any OCL expression can be used as the value for an attribute of the UML metaclass Expression or one of its subtypes. In
that case, the semantics section describes the meaning of the expression. A special subclass of Expression, called
ExpressionInOcl is used for this purpose. See Section 12.1, “Introduction,” on page 155 for a definition.
7.4
Basic Values and Types
In OCL, a number of basic types are predefined and available to the modeler at all time. These predefined value types are
independent of any object model and part of the definition of OCL.
The most basic value in OCL is a value of one of the basic types. The basic types of OCL, with corresponding examples
of their values, are shown in Table 2
Table 2 - Basic Types
type
values
Boolean
true, false
Integer
1, -5, 2, 34, 26524, ...
Real
1.5, 3.14, ...
String
'To be or not to be...'
OCL defines a number of operations on the predefined types. Table 3 gives some examples of the operations on the
predefined types. See Section 11.4, “Primitive Types,” on page 136 for a complete list of all operations.
Table 3 - Operations on predefined types
10
type
operations
Integer
*, +, -, /, abs()
Real
*, +, -, /, floor()
Table 3 - Operations on predefined types
type
operations
Boolean
and, or, xor, not, implies, if-then-else
String
concat(), size(), substring()
Collection, Set, Bag, Sequence and Tuple are basic types as well. Their specifics will be described in the upcoming
sections.
7.4.1
Types from the UML Model
Each OCL expression is written in the context of a UML model, a number of classifiers (types/classes, ...), their features
and associations, and their generalizations. All classifiers from the UML model are types in the OCL expressions that are
attached to the model.
7.4.2
Enumeration Types
Enumerations are Datatypes in UML and have a name, just like any other Classifier. An enumeration defines a number of
enumeration literals, that are the possible values of the enumeration. Within OCL one can refer to the value of an
enumeration. When we have Datatype named Gender in the example model with values 'female' or 'male' they can be used
as follows:
context Person inv: gender = Gender::male
7.4.3
Let Expressions
Sometimes a sub-expression is used more than once in a constraint. The let expression allows one to define a variable
which can be used in the constraint.
context Person inv:
let income : Integer = self.job.salary->sum() in
if isUnemployed then
income < 100
else
income >= 100
endif
A let expression may be included in any kind of OCL expression. It is only known within this specific expression.
7.4.4
Additional operations/attributes through «definition» expressions
The Let expression allows a variable to be used in one Ocl expression. To enable reuse of variables/operations over
multiple OCL expressions one can use a Constraint with the stereotype «definition», in which helper variables/operations
are defined. This «definition» Constraint must be attached to a Classifier and may only contain variable and/or operation
definitions, nothing else. All variables and operations defined in the «definition» constraint are known in the same context
as where any property of the Classifier can be used. Such variables and operations are attributes and operations with
stereotype «OclHelper» of the classifier. They are used in an OCL expression in exactly the same way as normal
attributes or operations are used. The syntax of the attribute or operation definitions is similar to the Let expression, but
each attribute and operation definition is prefixed with the keyword ’def’ as shown below.
11
context Person
def: income : Integer = self.job.salary->sum()
def: nickname : String = ’Little Red Rooster’
def: hasTitle(t : String) : Boolean = self.job->exists(title = t)
The names of the attributes / operations in a let expression may not conflict with the names of respective attributes/
associationEnds and operations of the Classifier.
Using this definition syntax is identical to defining an attribute/operation in the UML with stereotype «OclHelper» with
an attached OCL constraint for its derivation.
7.4.5
Type Conformance
OCL is a typed language and the basic value types are organized in a type hierarchy. This hierarchy determines
conformance of the different types to each other. You cannot, for example, compare an Integer with a Boolean or a String.
An OCL expression in which all the types conform is a valid expression. An OCL expression in which the types don’t
conform is an invalid expression. It contains a type conformance error. A type type1 conforms to a type type2 when an
instance of type1 can be substituted at each place where an instance of type2 is expected. The type conformance rules for
types in the class diagrams are simple.
• Each type conforms to each of its supertypes.
• Type conformance is transitive: if type1 conforms to type2, and type2 conforms to type3, then type1 conforms to type3.
The effect of this is that a type conforms to its supertype, and all the supertypes above. The type conformance rules for
the types from the OCL Standard Library are listed in Table 4.
Table 4 - Type conformance rules
Type
Conforms to/Is a subtype of
Condition
Set(T1)
Collection(T2)
if T1 conforms to T2
Sequence(T1)
Collection(T2)
Bag(T1)
Collection(T2)
Integer
Real
The conformance relation between the collection types only holds if they are collections of element types that conform to
each other. See Section 7.5.13, “Collection Type Hierarchy and Type Conformance Rules,” on page 23 for the complete
conformance rules for collections.
12
Table 5 provides examples of valid and invalid expressions.
Table 5 - Valid Expressions
7.4.6
OCL expression
valid
explanation
1 + 2 * 34
yes
1 + 'motorcycle'
no
type String does not conform to type
Integer
23 * false
no
type Boolean does not conform to Integer
12 + 13.5
yes
Re-typing or Casting
In some circumstances, it is desirable to use a property of an object that is defined on a subtype of the current known type
of the object. Because the property is not defined on the current known type, this results in a type conformance error.
When it is certain that the actual type of the object is the subtype, the object can be re-typed using the operation
oclAsType(OclType). This operation results in the same object, but the known type is the argument OclType. When there
is an object object of type Type1 and Type2 is another type, it is allowed to write:
object.oclAsType(Type2) --- evaluates to object with type Type2
An object can only be re-typed to one of its subtypes; therefore, in the example, Type2 must be a subtype of Type1.
If the actual type of the object is not a subtype of the type to which it is re-typed, the expression is undefined (see
(“Undefined Values”)).
7.4.7
Precedence Rules
The precedence order for the operations, starting with highest precedence, in OCL is:
• @pre
• dot and arrow operations: ‘.’ and ‘->’
• unary ‘not’ and unary minus ‘-’
• ‘*’ and ‘/’
• ‘+’ and binary ‘-’
• ‘if-then-else-endif’
• ‘<’, ‘>’, ‘<=’, ‘>=’
• ‘=’, ‘<>’
• ‘and’, ‘or’ and ‘xor’
• ‘implies’
Parentheses ‘(’ and ‘)’ can be used to change precedence.
13
7.4.8
Use of Infix Operators
The use of infix operators is allowed in OCL. The operators ‘+’, ‘-’, ‘*’. ‘/’, ‘<‘, ‘>’, ‘<>’ ‘<=’ ‘>=’ are used as infix
operators. If a type defines one of those operators with the correct signature, they will be used as infix operators. The
expression:
a+b
is conceptually equal to the expression:
a.+(b)
that is, invoking the ‘+’ operation on a with b as the parameter to the operation.
The infix operators defined for a type must have exactly one parameter. For the infix operators ‘<‘, ‘>’, ‘<=’, ‘>=’, ‘<>’,
‘and’, ‘or’, and ‘xor’ the return type must be Boolean.
7.4.9
Keywords
Keywords in OCL are reserved words. That means that the keywords cannot occur anywhere in an OCL expression as the
name of a package, a type or a property. The list of keywords is shown below:
and
attr
context
def
else
endif
endpackage
if
implies
in
inv
let
not
oper
or
package
post
pre
then
xor
7.4.10 Comment
Comments in OCL are written following two successive dashes (minus signs). Everything immediately following the two
dashes up to and including the end of line is part of the comment. For example:
-- this is a comment
14
Undefined Values
Some expressions will, when evaluated, have an undefined value. For instance, typecasting with oclAsType() to a type
that the object does not support or getting the ->first() element of an empty collection will result in undefined. In general,
an expression where one of the parts is undefined will itself be undefined. There are some important exceptions to this
rule, however. First, there are the logical operators:
• True OR-ed with anything is True
• False AND-ed with anything is False
• False IMPLIES anything is True
• anything IMPLIES True is True
The rules for OR and AND are valid irrespective of the order of the arguments and they are valid whether the value of the
other sub-expression is known or not.
The IF-expression is another exception. It will be valid as long as the chosen branch is valid, irrespective of the value of
the other branch.
Finally, there is an explicit operation for testing if the value of an expression is undefined. oclIsUndefined() is an
operation on OclAny that results in True if its argument is undefined and False otherwise.
7.5
Objects and Properties
OCL expressions can refer to Classifiers, e.g. types, classes, interfaces, associations (acting as types) and datatypes. Also
all attributes, association-ends, methods, and operations without side-effects that are defined on these types, etc. can be
used. In a class model, an operation or method is defined to be side-effect-free if the isQuery attribute of the operations is
true. For the purpose of this document, we will refer to attributes, association-ends, and side-effect-free methods and
operations as being properties. A property is one of:
• an Attribute
• an AssociationEnd
• an Operation with isQuery being true
• a Method with isQuery being true
The value of a property on an object that is defined in a class diagram is specified in an OCL expression by a dot
followed by the name of the property.
context Person inv:
self.isMarried
If self is a reference to an object, then self.property is the value of the property property on self.
7.5.1
Properties: Attributes
For example, the age of a Person is written as self.age:
context Person inv:
self.age > 0
15
The value of the subexpression self.age is the value of the age attribute on the particular instance of Person identified by
self. The type of this subexpression is the type of the attribute age, which is the standard type Integer.
Using attributes, and operations defined on the basic value types, we can express calculations etc. over the class model.
For example, a business rule might be “the age of a Person is always greater than zero.” This can be stated by the
invariant above.
Attributes may have multiplicities in a UML model. Wheneven the multiplicity of an attribute is greater than 1, the result
type is collection of values. Collections in OCL are described later in this chapter.
7.5.2
Properties: Operations
Operations may have parameters. For example, as shown earlier, a Person object has an income expressed as a function
of the date. This operation would be accessed as follows, for a Person aPerson and a date aDate:
aPerson.income(aDate)
The result of this operation call is a value of the return type of the operation, which is Integer in this example. If the
operation has out or in/out parameters, the result of this operation is a tuple containing all out, in/out parameters and the
return value. For example, if the income operation would have an out parameter bonus, the result of the above operation
call is of type Tuple( bonus: Integer, result: Integer). You can access these values using the names of the out
parameters, and the keyword result, for example:
aPerson.income(aDate).bonus = 300 and
aPerson.income(aDate).result = 5000
Note that the out parameters need not be included in the operation call. Values for all in or in/out parameters are
neccessary.
Defining operations
The operation itself could be defined by a postcondition constraint. This is a constraint that is stereotyped as
«postcondition». The object that is returned by the operation can be referred to by result. It takes the following form:
context Person::income (d: Date) : Integer
post: result = age * 1000
The right-hand-side of this definition may refer to the operation being defined (i.e., the definition may be recursive) as
long as the recursion is not infinite. Inside a pre- or postcondition one can also use the parameters of the operation. The
type of result, when the operation has no out or in/out parameters, is the return type of the operation, which is Integer in
the above example. When the operation does have out or in/out parameters, the return type is a Tuple as explained above.
The postcondition for the income operation with out parameter bonus may take the following form:
context Person::income (d: Date, bonus: Integer) : Integer
post: result = Tuple { bonus = ...,
result = .... }
To refer to an operation or a method that doesn’t take a parameter, parentheses with an empty argument list are
mandatory:
self.stockPrice() > 0
16
7.5.3
Properties: AssociationEnds and Navigation
Starting from a specific object, we can navigate an association on the class diagram to refer to other objects and their
properties. To do so, we navigate the association by using the opposite association-end:
object.associationEndName
The value of this expression is the set of objects on the other side of the associationEndName association. If the
multiplicity of the association-end has a maximum of one (“0..1” or “1”), then the value of this expression is an object. In
the example class diagram, when we start in the context of a Company (i.e., self is an instance of Company), we can
write:
context Company
inv: self.manager.isUnemployed = false
inv: self.employee->notEmpty()
In the first invariant self.manager is a Person, because the multiplicity of the association is one. In the second invariant
self.employee will evaluate in a Set of Persons. By default, navigation will result in a Set. When the association on the
Class Diagram is adorned with {ordered}, the navigation results in an OrderedSet.
Collections, like Sets, OrderedSets, Bags, and Sequences are predefined types in OCL. They have a large number of
predefined operations on them. A property of the collection itself is accessed by using an arrow ‘->’ followed by the name
of the property. The following example is in the context of a person:
context Person inv:
self.employer->size() < 3
This applies the size property on the Set self.employer, which results in the number of employers of the Person self.
context Person inv:
self.employer->isEmpty()
This applies the isEmpty property on the Set self.employer. This evaluates to true if the set of employers is empty and
false otherwise.
Missing AssociationEnd names
When the name of an association-end is missing at one of the ends of an association, the name of the type at the
association end tarting with a lowercase character is used as the rolename. If this results in an ambiguity, the rolename is
mandatory. This is e.g. the case with unnamed rolenames in reflexive associations. If the rolename is ambiguous, then it
cannot be used in OCL.
Navigation over Associations with Multiplicity Zero or One
Because the multiplicity of the role manager is one, self.manager is an object of type Person. Such a single object can be
used as a Set as well. It then behaves as if it is a Set containing the single object. The usage as a set is done through the
arrow followed by a property of Set. This is shown in the following example:
self.manager->size() = 1
The sub-expression self.manager is used as a Set, because the arrow is used to access the size property on Set. This
expression evaluates to true.
self.manager->foo
17
The sub-expression self.manager is used as Set, because the arrow is used to access the foo property on the Set. This
expression is incorrect, because foo is not a defined property of Set.
self.manager.age > 40
The sub-expression self.manager is used as a Person, because the dot is used to access the age property of Person.
In the case of an optional (0..1 multiplicity) association, this is especially useful to check whether there is an object or not
when navigating the association. In the example we can write:
context Person inv:
self.wife->notEmpty() implies self.wife.gender = Gender::female
Combining Properties
Properties can be combined to make more complicated expressions. An important rule is that an OCL expression always
evaluates to a specific object of a specific type. After obtaining a result, one can always apply another property to the
result to get a new result value. Therefore, each OCL expression can be read and evaluated left-to-right.
Following are some invariants that use combined properties on the example class diagram:
[1] Married people are of age >= 18
context Person inv:
self.wife->notEmpty() implies self.wife.age >= 18 and
self.husband->notEmpty() implies self.husband.age >= 18
[2] a company has at most 50 employees
self.employee->size() <= 50
7.5.4
Navigation to Association Classes
To specify navigation to association classes (Job and Marriage in the example), OCL uses a dot and the name of the
association class starting with a lowercase character:
context Person inv:
self.job
The sub-expression self.job evaluates to a Set of all the jobs a person has with the companies that are his/her employer. In
the case of an association class, there is no explicit rolename in the class diagram. The name job used in this navigation
is the name of the association class starting with a lowercase character, similar to the way described in the section
“Missing AssociationEnd names” above.
18
In case of a recursive association, that is an association of a class with itself, the name of the association class alone is not
enough. We need to distinguish the direction in which the association is navigated as well as the name of the association
class. Take the following model as an example.
bosses
Person
age
*
employees *
EmployeeRanking
score
Figure 2 - Navigating recursive association classes
When navigating to an association class such as employeeRanking there are two possibilities depending on the direction.
For instance, in the above example, we may navigate towards the employees end, or the bosses end. By using the name of
the association class alone, these two options cannot be distinguished. To make the distinction, the rolename of the
direction in which we want to navigate is added to the association class name, enclosed in square brackets. In the
expression
context Person inv:
self.employeeRanking[bosses]->sum() > 0
the self.employeeRanking[bosses] evaluates to the set of EmployeeRankings belonging to the collection of bosses. And in
the expression
context Person inv:
self.employeeRanking[employees]->sum() > 0
the self.employeeRanking[employees] evaluates to the set of EmployeeRankings belonging to the collection of employees.
The unqualified use of the association class name is not allowed in such a recursive situation. Thus, the following
example is invalid:
context Person inv:
self.employeeRanking->sum() > 0 -- INVALID!
In a non-recursive situation, the association class name alone is enough, although the qualified version is allowed as well.
Therefore, the examples at the start of this section could also be written as:
context Person inv:
self.job[employer]
7.5.5
Navigation from Association Classes
We can navigate from the association class itself to the objects that participate in the association. This is done using the
dot-notation and the role-names at the association-ends.
context Job
inv: self.employer.numberOfEmployees >= 1
inv: self.employee.age > 21
Navigation from an association class to one of the objects on the association will always deliver exactly one object. This
is a result of the definition of AssociationClass. Therefore, the result of this navigation is exactly one object, although it
can be used as a Set using the arrow (->).
19
7.5.6
Navigation through Qualified Associations
Qualified associations use one or more qualifier attributes to select the objects at the other end of the association. To
navigate them, we can add the values for the qualifiers to the navigation. This is done using square brackets, following the
role-name. It is permissible to leave out the qualifier values, in which case the result will be all objects at the other end of
the association. The following example results in a Set(Person) containing all customers of the Bank.
context Bank inv:
self.customer
The next example results in one Person, having account number 8764423.
context Bank inv:
self.customer[8764423]
If there is more than one qualifier attribute, the values are separated by commas, in the order which is specified in the
UML class model. It is not permissible to partially specify the qualifier attribute values.
7.5.7
Using Pathnames for Packages
Within UML, types are organized in packages. OCL provides a way of explicitly referring to types in other packages by
using a package-pathname prefix. The syntax is a package name, followed by a double colon:
Packagename::Typename
This usage of pathnames is transitive and can also be used for packages within packages:
Packagename1::Packagename2::Typename
7.5.8
Accessing overridden properties of supertypes
Whenever properties are redefined within a type, the property of the supertypes can be accessed using the oclAsType()
operation. Whenever we have a class B as a subtype of class A, and a property p1 of both A and B, we can write:
context B inv:
self.oclAsType(A).p1 -- accesses the p1 property defined in A
self.p1
-- accesses the p1 property defined in B
Figure 3 shows an example where such a construct is needed. In this model fragment there is an ambiguity with the OCL
expression on Dependency:
context Dependency inv:
self.source <> self
This can either mean normal association navigation, which is inherited from ModelElement, or it might also mean
navigation through the dotted line as an association class. Both possible navigations use the same role-name, so this is
always ambiguous. Using oclAsType() we can distinguish between them with:
context Dependency
inv: self.oclAsType(Dependency).source->isEmpty()
inv: self.oclAsType(ModelElement).source->isEmpty()
20
source
*
targ et
M od elE lem en t
*
....
N ote
D ep en den cy
v alu e: U n in terp rete d
Figure 3 - Accessing Overridden Properties Example
7.5.9
Predefined properties on All Objects
There are several properties that apply to all objects, and are predefined in OCL. These are:
oclIsTypeOf (t : OclType) : Boolean
oclIsKindOf (t : OclType) : Boolean
oclInState (s : OclState) : Boolean
oclIsNew ()
: Boolean
oclAsType (t : OclType) : instance of OclType
The operation is oclIsTypeOf results in true if the type of self and t are the same. For example:
context Person
inv: self.oclIsTypeOf( Person ) -- is true
inv: self.oclIsTypeOf( Company) -- is false
The above property deals with the direct type of an object. The oclIsKindOf property determines whether t is either the
direct type or one of the supertypes of an object.
The operation oclInState(s) results in true if the object is in the state s. Values for s are the names of the states in the
statemachine(s) attached to the Classifier of object. For nested states the statenames can be combined using the double
colon ‘::’ .
On
Off
Standby
NoPower
21
In the example statemachine above, values for s can be On, Off, Off::Standby, Off::NoPower. If the classifier of object has
the above associated statemachine valid OCL expressions are:
object.oclInState(On)
object.oclInState(Off)
object.oclInstate(Off::Standby)
object.oclInState(Off::NoPower)
If there are multiple statemachines attached to the object’s classifier, then the statename can be prefixed with the name of
the statemachine containing the state and the double colon ‘::’, as with nested states.
The operation oclIsNew evaluates to true if, used in a postcondition, the object is created during performing the operation.
i.e., it didn’t exist at precondition time.
7.5.10 Features on Classes Themselves
All properties discussed until now in OCL are properties on instances of classes. The types are either predefined in OCL
or defined in the class model. In OCL, it is also possible to use features defined on the types/classes themselves. These
are, for example, the class-scoped features defined in the class model. Furthermore, several features are predefined on
each type.
A predefined feature on classes, interfaces and enumerations is allInstances, which results in the Set of all instances of the
type in existence at the specific time when the expression is evaluated. If we want to make sure that all instances of
Person have unique names, we can write:
context Person inv:
Person.allInstances()->forAll(p1, p2 |
p1 <> p2 implies p1.name <> p2.name)
The Person.allInstances() is the set of all persons and is of type Set(Person). It is the set of all persons that exist in the
system at the time that the expression is evaluated.
7.5.11 Collections
Single navigation of an association results in a Set, combined navigations in a Bag, and navigation over associations
adorned with {ordered} results in an OrderedSet. Therefore, the collection types define in the OCL Standard Library play
an important role in OCL expressions.
The type Collection is predefined in OCL. The Collection type defines a large number of predefined operations to enable
the OCL expression author (the modeler) to manipulate collections. Consistent with the definition of OCL as an
expression language, collection operations never change collections; isQuery is always true. They may result in a
collection, but rather than changing the original collection they project the result into a new one.
Collection is an abstract type, with the concrete collection types as its subtypes. OCL distinguishes three different
collection types: Set, Sequence, and Bag. A Set is the mathematical set. It does not contain duplicate elements. A Bag is
like a set, which may contain duplicates (i.e., the same element may be in a bag twice or more). A Sequence is like a Bag
in which the elements are ordered. Both Bags and Sets have no order defined on them.
Collection Literals
Sets, Sequences, and Bags can be specified by a literal in OCL. Curly brackets surround the elements of the collection,
elements in the collection are written within, separated by commas. The type of the collection is written before the curly
brackets:
22
Set { 1 , 2 , 5 , 88 }
Set { 'apple' , 'orange', 'strawberry' }
A Sequence:
Sequence { 1, 3, 45, 2, 3 }
Sequence { 'ape', 'nut' }
A bag:
Bag {1 , 3 , 4, 3, 5 }
Because of the usefulness of a Sequence of consecutive Integers, there is a separate literal to create them. The elements
inside the curly brackets can be replaced by an interval specification, which consists of two expressions of type Integer,
Int-expr1 and Int-expr2, separated by ‘..’. This denotes all the Integers between the values of Int-expr1 and Int-expr2,
including the values of Int-expr1 and Int-expr2 themselves:
Sequence{ 1..(6 + 4) }
Sequence{ 1..10 }
-- are both identical to
Sequence{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
The complete list of Collection operations is described in chapter 11 (“The OCL Standard Library”).
Collections can be specified by a literal, as described above. The only other way to get a collection is by navigation. To
be more precise, the only way to get a Set, OrderedSet, Sequence, or Bag is:
1.
a literal, this will result in a Set, OrderedSet, Sequence, or Bag:
Set
{2 , 4, 1 , 5 , 7 , 13, 11, 17 }
OrderedSet {1 , 2, 3 , 5 , 7 , 11, 13, 17 }
Sequence {1 , 2, 3 , 5 , 7 , 11, 13, 17 }
Bag
{1, 2, 3, 2, 1}
2.
a navigation starting from a single object can result in a collection:
self.employee
3.
operations on collections may result in new collections:
collection1->union(collection2)
7.5.12 Collections of Collections
In UML 1.4 a collection in OCL was always flattened, i.e. a collection could never contain other collections as elements.
This restriction is relieved in UML 2.0. OCL allows elements of collections to be collections themselves. The OCL
Standard Library includes specific flatten operations for collections. These can be used to flatten collections of collections
explicitly.
7.5.13 Collection Type Hierarchy and Type Conformance Rules
In addition to the type conformance rules in 7.4.5 (“Type Conformance”), the following rules hold for all types, including
the collection types:
•
The types Set (X), Bag (X) and Sequence (X) are all subtypes of Collection (X).
Type conformance rules are as follows for the collection types:
23
•
Type1 conforms to Type2 when they are identical (standard rule for all types).
•
Type1 conforms to Type2 when it is a subtype of Type2 (standard rule for all types).
•
Collection(Type1) conforms to Collection(Type2), when Type1 conforms to Type2. This is also true for Set(Type1)/
Set(Type2), Sequence(Type1)/Sequence(Type2), Bag(Type1)/Bag(Type2)
•
Type conformance is transitive: if Type1 conforms to Type2, and Type2 conforms to Type3, then Type1 conforms to
Type3 (standard rule for all types).
For example, if Bicycle and Car are two separate subtypes of Transport:
Set(Bicycle) conforms to Set(Transport)
Set(Bicycle) conforms to Collection(Bicycle)
Set(Bicycle) conforms to Collection(Transport)
Note that Set(Bicycle) does not conform to Bag(Bicycle), nor the other way around. They are both subtypes of
Collection(Bicycle) at the same level in the hierarchy.
7.5.14 Previous Values in Postconditions
As stated in 7.3.4 (“Pre- and Postconditions”), OCL can be used to specify pre- and post-conditions on operations and
methods in UML. In a postcondition, the expression can refer to values for each property of an object at two moments in
time:
• the value of a property at the start of the operation or method
• the value of a property upon completion of the operation or method
The value of a property in a postcondition is the value upon completion of the operation. To refer to the value of a
property at the start of the operation, one has to postfix the property name with the keyword ‘@pre’:
context Person::birthdayHappens()
post: age = age@pre + 1
The property age refers to the property of the instance of Person which executes the operation. The property age@pre
refers to the value of the property age of the Person that executes the operation, at the start of the operation.
If the property has parameters, the ‘@pre’ is postfixed to the propertyname, before the parameters.
context Company::hireEmployee(p : Person)
post: employees = employees@pre->including(p) and
stockprice() = stockprice@pre() + 10
When the pre-value of a property evaluates to an object, all further properties that are accessed of this object are the new
values (upon completion of the operation) of this object. So:
a.b@pre.c
-- takes the old value of property b of a, say x
-- and then the new value of c of x.
a.b@pre.c@pre -- takes the old value of property b of a, say x
-- and then the old value of c of x.
The ‘@pre’ postfix is allowed only in OCL expressions that are part of a Postcondition. Asking for a current property of
an object that has been destroyed during execution of the operation results in OclUndefined. Also, referring to the
previous value of an object that has been created during execution of the operation results in OclUndefined.
24
7.5.15 Tuples
It is possible to compose several values into a tuple. A tuple consists of named parts, each of which can have a distinct
type. Some examples of tuples are:
Tuple {name: String = ‘John’, age: Integer = 10}
Tuple {a: Collection(Integer) = Set{1, 3, 4}, b: String = ‘foo’, c: String = ‘bar’}
This is also the way to write tuple literals in OCL; they are enclosed in curly brackets, and the parts are separated by
commas. The type names are optional, and the order of the parts is unimportant. Thus:
Tuple {name: String = ‘John’, age: Integer = 10} is equivalent to
Tuple {name = ‘John’, age = 10} and to
Tuple {age = 10, name = ‘John’}
Also, note that the values of the parts may be given by arbitrary OCL expressions, so for example we may write:
context Person def:
attr statistics : Set(TupleType(company: Company, numEmployees: Integer,
wellpaidEmployees: Set(Person), totalSalary: Integer)) =
managedCompanies->collect(c |
Tuple { company: Company = c,
numEmployees: Integer = c.employee->size(),
wellpaidEmployees: Set(Person) = c.job->select(salary>10000).employee->asSet(),
totalSalary: Integer = c.job.salary->sum()
}
)
This results in a bag of tuples summarizing the company, number of employees, the best paid employees and total salary
costs of each company a person manages.
The parts of a tuple are accessed by their names, using the same dot notation that is used for accessing attributes. Thus:
Tuple {x: Integer = 5, y: String = ‘hi’}.x = 5
is a true, if somewhat pointless, expression. Using the definition of statistics above, we can write:
context Person inv:
statistics->sortedBy(totalSalary)->last().wellpaidEmployees->includes(self)
This asserts that a person is one of the best-paid employees of the company with the highest total salary that he manages.
In this expression, both ‘totalSalary’ and ‘wellpaidEmployees’ are accessing tuple parts.
7.6
Collection Operations
OCL defines many operations on the collection types. These operations are specifically meant to enable a flexible and
powerful way of projecting new collections from existing ones. The different constructs are described in the following
sections.
7.6.1
Select and Reject Operations
Sometimes an expression using operations and navigations results in a collection, while we are interested only in a special
subset of the collection. OCL has special constructs to specify a selection from a specific collection. These are the select
and reject operations. The select specifies a subset of a collection. A select is an operation on a collection and is specified
using the arrow-syntax:
25
collection->select( ... )
The parameter of select has a special syntax that enables one to specify which elements of the collection we want to
select. There are three different forms, of which the simplest one is:
collection->select( boolean-expression )
This results in a collection that contains all the elements from collection for which the boolean-expression evaluates to
true. To find the result of this expression, for each element in collection the expression boolean-expression is evaluated.
If this evaluates to true, the element is included in the result collection, otherwise not. As an example, the following OCL
expression specifies that the collection of all the employees older than 50 years is not empty:
self.employee->select(age > 50)->notEmpty()
The self.employee is of type Set(Person). The select takes each person from self.employee and evaluates age > 50 for this
person. If this results in true, then the person is in the result Set.
As shown in the previous example, the context for the expression in the select argument is the element of the collection
on which the select is invoked. Thus the age property is taken in the context of a person.
In the above example, it is impossible to refer explicitly to the persons themselves; you can only refer to properties of
them. To enable to refer to the persons themselves, there is a more general syntax for the select expression:
collection->select( v | boolean-expression-with-v )
The variable v is called the iterator. When the select is evaluated, v iterates over the collection and the booleanexpression-with-v is evaluated for each v. The v is a reference to the object from the collection and can be used to refer to
the objects themselves from the collection. The two examples below are identical:
self.employee->select(age > 50)->notEmpty()
self.employee->select(p | p.age > 50)->notEmpty()
The result of the complete select is the collection of persons p for which the p.age > 50 evaluates to True. This amounts
to a subset of self.employee.
As a final extension to the select syntax, the expected type of the variable v can be given. The select now is written as:
collection->select( v : Type | boolean-expression-with-v )
The meaning of this is that the objects in collection must be of type Type. The next example is identical to the previous
examples:
self.employee.select(p : Person | p.age > 50)->notEmpty()
The compete select syntax now looks like one of:
collection->select( v : Type | boolean-expression-with-v )
collection->select( v | boolean-expression-with-v )
collection->select( boolean-expression )
The reject operation is identical to the select operation, but with reject we get the subset of all the elements of the
collection for which the expression evaluates to False. The reject syntax is identical to the select syntax:
collection->reject( v : Type | boolean-expression-with-v )
collection->reject( v | boolean-expression-with-v )
26
collection->reject( boolean-expression )
As an example, specify that the collection of all the employees who are not married is empty:
self.employee->reject( isMarried )->isEmpty()
The reject operation is available in OCL for convenience, because each reject can be restated as a select with the negated
expression. Therefore, the following two expressions are identical:
collection->reject( v : Type | boolean-expression-with-v )
collection->select( v : Type | not (boolean-expression-with-v) )
7.6.2
Collect Operation
As shown in the previous section, the select and reject operations always result in a sub-collection of the original
collection. When we want to specify a collection which is derived from some other collection, but which contains
different objects from the original collection (i.e., it is not a sub-collection), we can use a collect operation. The collect
operation uses the same syntax as the select and reject and is written as one of:
collection->collect( v : Type | expression-with-v )
collection->collect( v | expression-with-v )
collection->collect( expression )
The value of the reject operation is the collection of the results of all the evaluations of expression-with-v.
An example: specify the collection of birthDates for all employees in the context of a company. This can be written in the
context of a Company object as one of:
self.employee->collect( birthDate )
self.employee->collect( person | person.birthDate )
self.employee->collect( person : Person | person.birthDate )
An important issue here is that the resulting collection is not a Set, but a Bag. When more than one employee has the
same value for birthDate, this value will be an element of the resulting Bag more than once. The Bag resulting from the
collect operation always has the same size as the original collection.
It is possible to make a Set from the Bag, by using the asSet property on the Bag. The following expression results in the
Set of different birthDates from all employees of a Company:
self.employee->collect( birthDate )->asSet()
Shorthand for Collect
Because navigation through many objects is very common, there is a shorthand notation for the collect that makes the
OCL expressions more readable. Instead of
self.employee->collect(birthdate)
we can also write:
self.employee.birthdate
In general, when we apply a property to a collection of Objects, then it will automatically be interpreted as a collect over
the members of the collection with the specified property.
For any propertyname that is defined as a property on the objects in a collection, the following two expressions are
identical:
27
collection.propertyname
collection->collect(propertyname)
and so are these if the property is parameterized:
collection.propertyname (par1, par2, ...)
collection->collect (propertyname(par1, par2, ...))
7.6.3
ForAll Operation
Many times a constraint is needed on all elements of a collection. The forAll operation in OCL allows specifying a
Boolean expression, which must hold for all objects in a collection:
collection->forAll( v : Type | boolean-expression-with-v )
collection->forAll( v | boolean-expression-with-v )
collection->forAll( boolean-expression )
This forAll expression results in a Boolean. The result is true if the boolean-expression-with-v is true for all elements of
collection. If the boolean-expression-with-v is false for one or more v in collection, then the complete expression
evaluates to false. For example, in the context of a company:
context Company
self.employee->forAll( age <= 65 )
inv:
inv:
self.employee->forAll( p | p.age <= 65 )
inv:
self.employee->forAll( p : Person | p.age <= 65 )
These invariants evaluate to true if the age property of each employee is less or equal to 65.
The forAll operation has an extended variant in which more then one iterator is used. Both iterators will iterate over the
complete collection. Effectively this is a forAll on the Cartesian product of the collection with itself.
self.employee->forAll( e1, e2 : Person |
e1 <> e2 implies e1.forename <> e2.forename)
This expression evaluates to true if the forenames of all employees are different. It is semantically equivalent to:
self.employee->forAll (e1 | self.employee->forAll (e2 |
e1 <> e2 implies e1.forename <> e2.forename))
7.6.4
Exists Operation
Many times one needs to know whether there is at least one element in a collection for which a constraint holds. The
exists operation in OCL allows you to specify a Boolean expression which must hold for at least one object in a
collection:
collection->exists( v : Type | boolean-expression-with-v )
collection->exists( v | boolean-expression-with-v )
collection->exists( boolean-expression )
This exists operation results in a Boolean. The result is true if the boolean-expression-with-v is true for at least one
element of collection. If the boolean-expression-with-v is false for all v in collection, then the complete expression
evaluates to false. For example, in the context of a company:
self.employee->exists( forename = 'Jack' )
28
self.employee->exists( p | p.forename = 'Jack' )
self.employee->exists( p : Person | p.forename = 'Jack' )
These expressions evaluate to true if the forename property of at least one employee is equal to ‘Jack.’
7.6.5
Iterate Operation
The iterate operation is slightly more complicated, but is very generic. The operations reject, select, forAll, exists, collect,
can all be described in terms of iterate. An accumulation builds one value by iterating over a collection.
collection->iterate( elem : Type; acc : Type = <expression> |
expression-with-elem-and-acc )
The variable elem is the iterator, as in the definition of select, forAll, etc. The variable acc is the accumulator. The
accumulator gets an initial value <expression>. When the iterate is evaluated, elem iterates over the collection and the
expression-with-elem-and-acc is evaluated for each elem. After each evaluation of expression-with-elem-and-acc, its
value is assigned to acc. In this way, the value of acc is built up during the iteration of the collection. The collect
operation described in terms of iterate will look like:
collection->collect(x : T | x.property)
-- is identical to:
collection->iterate(x : T; acc : T2 = Bag{} |
acc->including(x.property))
Or written in Java-like pseudocode the result of the iterate can be calculated as:
iterate(elem : T; acc : T2 = value)
{
acc = value;
for(Enumeration e = collection.elements() ; e.hasMoreElements(); ){
elem = e.nextElement();
acc = <expression-with-elem-and-acc>
}
return acc;
}
Although the Java pseudo code uses a ‘next element’, the iterate operation is defined not only for Sequqnce, but for each
collection type. The order of the iteration through the elements in the collection is not defined for Set and Bag. For a
Sequence the order is the order of the elements in the sequence.
7.7
Messages in OCL
This section contains some examples of the concrete syntax and explains the finer details of the message expression. In
earlier versions the phrase "actions in OCL" was used, but message was found to capture the meaning more precisely.
7.7.1
Calling operations and sending signals
To specify that communication has taken place, the hasSent (‘^’) operator is used:
context Subject::hasChanged()
post: observerûpdate(12, 14)
29
The observerûpdate(12, 14) results in true if an update message with arguments 12 and 14 was sent to observer during
the execution of the operation. Update() is either an Operation that is defined in the class of observer, or it is a Signal
specified in the UML model. The argument(s) of the message expression (12 and 14 in this example) must conform to the
parameters of the operation/signal definition.
If the actual arguments of the operation/signal are not known, or not restricted in any way, it can be left unspecified. This
is shown by using a question mark. Following the question mark is an optional type, which may be needed to find the
correct operation when the same operation exists with different parameter types.
post: observerûpdate(? : Integer, ? : Integer)
This example states that the message update has been sent to observer, but that the values of the parameters are not
known.
OCL also defines a special OclMessage type. One can get the actual OclMessages through the message operator: ^^.
post: observer^ûpdate(12, 14)
This results in the Sequence of messages sent. Each element of the collection is an instance of OclMessage. In the
remainder of the constraint one can refer to the parameters of the operation using their formal parameter name from the
operation definition. If the operation update has been defined with formal parameters named i and j, then we can write:
post: let messages : Sequence(OclMessage) = observer^ûpdate(? : Integer, ? : Integer) in
messages->notEmpty() and
messages->exists( m | m.i > 0 and m.j >= m.i )
The value of the parameter i is not known, but it must be greater than zero and the value of parameter j must be larger or
equal to i..
Because the ^^ operator results in an instance of OclMessage, the message expression can also be used to specify
collections of messages sent to different targets. For an observer pattern we can write:
post: let messages : Sequence(OclMessage) =
observers->collect(o | o^ûpdate(? : Integer, ? : Integer) ) in
messages->forAll(m | m.i <= m.j )
Messages is now a set of OclMessage instances, where every OclMessage instance has one of the observers as a target.
7.7.2
Accessing result values
A signal sent message is by definition asynchronous, so there never is a return value. If there is a logical return value it
must be modeled as a separate signal message. Yet, for an operation call there is a potential return value. This is only
available if the operation has already returned (not neccesary if the operation call is aynchronous), and it specifies a return
type in its definition. The standard operation result() of OclMessage contains the return value of the called operation. If
getMoney(...) is an operation on Company that returns a boolean, as in Company::getMoney(amount : Integer) :
Boolean, we can write:
context Person::giveSalary(amount : Integer)
post: let message : OclMessage = company^getMoney(amount) in
message.hasReturned()
-- getMoney was sent and returned
and
message.result() = true
-- the getMoney call returned true
30
As with the previous example we can also access a collection of return values from a collection of OclMessages. If
message.hasReturned() is false, then message.result() will be undefined.
7.7.3
An example
This section shows an example of using the OCL message expression.
The Example and Problem
Suppose we have build a component, which takes any form of input and transforms it into garbage (aka encrypts it). The
component GarbageCan uses an interface UsefulInformationProvider which must be implemented by users of the
component to provide the input. The operation getNextPieceOfGarbage of GarbageCan can then be used to retrieve the
garbled data. Figure 4 shows the component’s class diagram. Note that none of the operations are marked as queries.
G arbageCan
setUsefulInform ationProvider(uip : UsefulInform ationProvider)
getNextPieceO fG arbage() : Integer
0..1
#datasource
<<Interface>>
UsefulInform ationProvider
getNextPieceO fData() : Integer
Figure 4 - OclMessage Example
When selling the component, we do not want to give the source code to our customers. However, we want to specify the
component’s behavior as precisely as possible. So, for example, we want to specify, what getNextPieceOfGarbage does.
Note that we cannot write:
context GarbageCan::getNextPieceOfGarbage() : Integer
post: result = (datasource.getNextPieceOfData() * .7683425 + 10000) / 20 + 3
because UsefulInformationProvider::getNextPieceOfData() is not a query (e.g., it may increase some internal pointer
so that it can return the next piece of data at the next call). Still we would like to say something about how the garbage is
derived from the original data.
The solution
To solve this problem, we can use an OclMessage to represent the call to getNextPieceOfData. This allows us to check for
the result. Note that we need to demand that the call has returned before accessing the result:
context GarbageCan::getNextPieceOfGarbage() : Integer
post: let message : OclMessage = datasource^^getNextPieceOfData()->first() in
message.hasReturned()
and
result = (message.result() * .7683425 + 10000) / 20 + 3
31
7.8
Resolving Properties
For any property (attribute, operation, or navigation), the full notation includes the object of which the property is taken.
As seen in Section 7.3.3, self can be left implicit, and so can the iterator variables in collection operations. At any place
in an expression, when an iterator is left out, an implicit iterator-variable is introduced. For example in:
context Person inv:
employer->forAll( employee->exists( lastName = name) )
three implicit variables are introduced. The first is self, which is always the instance from which the constraint starts.
Secondly an implicit iterator is introduced by the forAll and third by the exists. The implicit iterator variables are
unnamed. The properties employer, employee, lastName and name all have the object on which they are applied left out.
Resolving these goes as follows:
•
at the place of employer there is one implicit variable: self : Person. Therefore employer must be a property of self.
•
at the place of employee there are two implicit variables: self : Person and iter1 : Company. Therefore employer
must be a property of either self or iter1. If employee is a property of both self and iter1 then it is defined to belong
to the variable in the most inner scope, which is iter1.
•
at the place of lastName and name there are three implicit variables: self : Person , iter1 : Company and iter2 : Person.
Therefore lastName and name must both be a property of either self or iter1 or iter2. In the UML model property name
is a property of iter1. However, lastName is a property of both self and iter2. This is ambiguous and therefore the lastName refers to the variable in the most inner scope, which is iter2.
Both of the following invariant constraint are correct, but have a different meaning:
context Person
inv: employer->forAll( employee->exists( p | p.lastName = name) )
inv: employer->forAll( employee->exists( self.lastName = name) )
32
8
Abstract Syntax
This section describes the abstract syntax of the OCL. In this abstract syntax a number of metaclasse from the UML
metamodel are imported. These metaclasses are shown in the models with the annotation ’(from <UML package>)’ and
shown with a transparant fill color. All metaclasses defined as part of the OCL abstract syntax are shown with a light gray
background.
8.1
Introduction
The abstract syntax as described below defines the concepts that are part of the OCL using a MOF compliant metamodel.
The abstract syntax is divided into several packages.
• The
Types package describes the concepts that define the type system of OCL. It shows which types are predefined in
OCL and which types are deduced from the UML models.
• The Expressions package describes the structure of OCL expressions.
8.2
The Types Package
OCL is a typed language. Each expression has a type which is either explicitly declared or can be statically derived.
Evaluation of the expression yields a value of this type. Therefore, before we can define expressions, we have to provide
a model for the concept of type. A metamodel for OCL types is shown in this section. Note that instances of the classes
in the metamodel are the types themselves (e.g. Integer) not instances of the domain they represent (e.g. -15, 0, 2, 3).
The model in Figure 5 shows the OCL types. The basic type is the UML Classifier, which includes all subtypes of
Classifier from the UML infrastructure.
In the model the CollectionType and its subclasses and the TupleType are special. One can never instantiate all collection
types, because there is an infinite number, especially when nested collections are taken in account. Users will never
instantiate these types explicitly. Conceptually all these types do exist, but such a type should be (lazily) instantiated by a
tool, whenever it is needed in an expression.
In comparison with UML 1.4 the type OclType has been removed from the type hierarchy. This means that a Classifier is
not a valid OCL expression any more.
33
StructuralFeature
0..n
(f rom Core)
+type
1
OclMessageType
Classifier
(fr om C ore )
Oc lModelElementType
+elementType
1
DataT ype
VoidType
(f rom Core)
TupleType
Primitive
0..4
+collectionTypes
SequenceType
BagType
(f rom Core)
SetType
0..1 +referredSignal
CollectionType
0..1 +referredOperation
Signal
Operation
(f rom Common Behavi...
(f rom Core)
OrderedSetType
Figure 5 - Abstract syntax kernel metamodel for OCL Types
BagType
BagType is a collection type which describes a multiset of elements where each element may occur multiple times in the
bag. The elements are unordered. Part of a BagType is the declaration of the type of its elements.
CollectionType
CollectionType describes a list of elements of a particular given type. CollectionType is an abstract class. Its concrete
subclasses are SetType, SequenceType and BagType types. Part of every collection type is the declaration of the type of
its elements, i.e. a collection type is parameterized with an element type. In the metamodel, this is shown as an
association from CollectionType to Classifier. Note that there is no restriction on the element type of a collection type.
This means in particular that a collection type may be parameterized with other collection types allowing collections to be
nested arbitrarily deep.
Associations
•
34
elementType
The type of the elements in a collection. All elements in a collection must conform to
this type.
OclMessageType
OclMessageType describe ocl messages. Like to the collection types, OclMessageType describes a set of types in the
standard library. Part of every OclMessageType is a reference to the declaration of the type of its operation or signal, i.e.
an ocl message type is parameterized with an operation or signal. In the metamodel, this is shown as an association from
OclMessageType to Operation and to Signal. OclMessageType is part of the abstract syntax of OCL, residing on M2
level. Its instances, called OclMessage, and subtypes of OclMessage, reside on M1 level.
Associations
•
referredSignal
The Signal that is sent by the message.
•
referredOperation
The Operation that is called by the message.
OclModelElementType
OclModelElementType represents the types of elements that are ModelElements in the UML metamodel. It is used to
be able to refer to states and classifiers in e.g. oclInState(...) and oclIsKindOf(...)
OrderedSetType
OrderedSetType is a collection type which describes a set of elements where each distinct element occurs only once in
the set. The elements are ordered by their position in the sequence. Part of an OrderedSetType is the declaration of the
type of its elements.
SequenceType
SequenceType is a collection type which describes a list of elements where each element may occur multiple times in the
sequence. The elements are ordered by their position in the sequence. Part of a SequenceType is the declaration of the
type of its elements.
SetType
SetType is a collection type which describes a set of elements where each distinct element occurs only once in the set.
The elements are not ordered. Part of a SetType is the declaration of the type of its elements.
TupleType
TupleType (informaly known as record type or struct) combines different types into a single aggregate type. The parts of
a TupleType are described by its attributes, each having a name and a type. There is no restriction on the kind of types
that can be used as part of a tuple. In particular, a TupleType may contain other tuple types and collection types. Each
attribute of a TupleType represents a single feature of a TupleType. Each part is to uniquely identified by its name.
VoidType
VoidType represents a type that conforms to all types. The only instance of VoidType is OclVoid, which is further defined
in the standard library. Furthermore OclVoid has exactly one instance called OclUndefined.
8.2.1
Type Conformance
The type conformance rules are formally underpinned in the Semantics section of the specification. To ensure that the
rules are accessible to UML modellers they are specified in this section using OCL. For this, the additional operation
conformsTo(c : Classifier) : Boolean is defined on Classifier. It evaluates to true, if the self Classifier conforms to the
argument c. The following OCL statements define type conformance for individual types.
35
BagType
[1] Different bag types conform to each other if their element types conform to each other.
context BagType
inv: BagType.allInstances()->forAll(b |
self.elementType.conformsTo(b.elementType) implies self.conformsTo(b))
Classifier
[1] Conformance is a transitive relationship.
context Classifier
inv Transitivity: Classifier.allInstances()->forAll(x|Classifier.allInstances()
->forAll(y|
(self.conformsTo(x) and x.conformsTo(y)) implies self.conformsTo(y)))
[2] All classifiers except collections conform to OclAny.
context Classifier
inv: (not self.oclIsKindOf (CollectionType)) implies
Primitive.allInstances()->forAll(p | (p.name = 'OclAny') implies self.conformsTo(p))
[3] Classes conform to superclasses and interfaces that they realize.
context Class
inv : self.generalization.parent->forAll (p |
(p.oclIsKindOf(Class) or p.oclIsKindOf(Interface)) implies
self.conformsTo(p.oclAsType(Classifier)))
[4] Interfaces conforms to super interfaces.
context Interface
inv : self.generalization.parent->forAll (p |
p.oclIsKindOf(Interface) implies self.conformsTo(p.oclAsType(Interface)))
[5] The Conforms operation between Types is reflexive, a Classifier always conform to itself.
context Classifier
inv: self.conformsTo(self)
[6] The Conforms operation between Types is anti-symmetric.
context Classifier
inv: Classifier.allInstances()->forAll(t1, t2 |
(t1.conformsTo(t2) and t2.conformsTo(t1)) implies t1 = t2)
CollectionType
[1] Specific collection types conform to collection type.
context CollectionType
inv: -- all instances of SetType, SequenceType, BagType conform to a
-- CollectionType if the elementTypes conform
CollectionType.allInstances()->forAll (c |
c.oclIsTypeOf(CollectionType) and
self.elementType.conformsTo(c.elementType) implies
self.conformsTo(c))
[2] Collections do not conform to any primitive type.
inv: Primitive.allInstances()->forAll (p | not self.conformsTo(p))
[3] Collections of non-conforming types do not conform.
36
inv: CollectionType.allInstances()->forAll (c |
(not self.elementType.conformsTo (c.elementType)) implies (not self.conformsTo (c)))
OrderedSetType
[1] Different ordered set types conform to each other if their element types conform to each other.
context OrderedSetType
inv: OrderedSetType.allInstances()->forAll(s |
self.elementType.conformsTo(s.elementType) implies self.conformsTo(s))
Primitive
[1] Integer conforms to real.
context Primitive
inv: (self.name = 'Integer') implies
Primitive.allInstances()->forAll (p | (p.name = 'Real') implies
(self.conformsTo(p))))
SequenceType
[1] Different sequence types conform to each other if their element types conform to each other.
context SequenceType
inv: SequenceType.allInstances()->forAll(s |
SetType
[1] Different set types conform to each other if their element types conform to each other.
context SetType
inv: SetType.allInstances()->forAll(s |
TupleType
[1] Tuple types conform to each other when their names and types conform to each other. Note that allAttributes is an additional operation in the UML 1.4.
context TupleType
inv: TupleType.allInstances()->forAll (t |
( t.allAttributes()->forAll (tp |
-- make sure at least one tuplepart has the same name
-- (uniqueness of tuplepart names will ensure that not two
-- tupleparts have the same name within one tuple)
self.allAttributes()->exists(stp|stp.name = tp.name) and
-- make sure that all tupleparts with the same name conforms.
self.allAttributes()->forAll(stp | (stp.name = tp.name) and
stp.type.conformsTo(tp.type))
)
implies
self.conformsTo(t)
))
VoidType
[1] Void conforms to all other types.
37
context VoidType
inv: Classifier.allInstances()->forAll (c | self.conformsTo (c))
8.2.2
Well-formedness Rules for the Types Package
BagType
[1] The name of a bag type is “Bag” followed by the element type’s name in parentheses.
context BagType
inv: self.name = ’Bag(’ + self.elementType.name + ’)’
CollectionType
[1] The name of a collection type is “Collection” followed by the element type’s name in parentheses.
inv: self.name = ’Collection(’ + self.elementType.name + ’)’
Classifier
[1] For each classifier at most one of each of the different collection types exist.
context Classifier
inv: collectionTypes->select(oclIsTypeOf(CollectionType))->size() <= 1
inv: collectionTypes->select(oclIsTypeOf(BagType
))->size() <= 1
inv: collectionTypes->select(oclIsTypeOf(SequenceType ))->size() <= 1
inv: collectionTypes->select(oclIsTypeOf(SetType
))->size() <= 1
OclMessageType
[1] OclMessageType has either a link with a Signal or with an operation, but not both.
context OclMessageType
inv: referredOperation->size() + referredSignal->size() = 1
[2] The parameters of the referredOperation become attributes of the instance of OclMessageType.
inv: referredOperation->size() = 1 implies
self.feature = referredOperation.parameter.asAttribute()
[3] The attributes of the referredSignal become attributes of the instance of OclMessageType.
inv: referredSignal->size() = 1 implies
self.feature = referredSignal.feature
OrderedSetType
[1] The name of a set type is “OrderedSet” followed by the element type’s name in parentheses.
context OrderedSetType
inv: self.name = ’OrderedSet(’ + self.elementType.name + ’)’
SequenceType
[1] The name of a sequence type is “Sequence” followed by the element type’s name in parentheses.
context SequenceType
inv: self.name = ’Sequence(’ + self.elementType.name + ’)’
38
SetType
[1] The name of a set type is “Set” followed by the element type’s name in parentheses.
context SetType
inv: self.name = ’Set(’ + self.elementType.name + ’)’
TupleType
[1] The name of a tuple type includes the names of the individual parts and the types of those parts.
context TupleType
inv: name =
’Tuple(’.concat (
Sequence{1..allAttributes()->size()}->iterate (pn; s: String = ’’ |
let p: Attribute = allAttributes()->at (pn) in (
s.concat (
(if (pn>1) then ’,’ else ’’ endif)
.concat (p.name).concat (’:’)
.concat (p.type.name)
)
)
)
).concat (’)’)
[2] All parts belonging to a tuple type have unique names.
context TupleType
inv: -- always true, because attributes must have unique names.
[3] A TupleType instance has only features that are Attributes (tuple parts).
context TupleType
inv: feature->forAll (f | f.oclIsTypeOf(Attribute))
39
8.3
The Expressions Package
This section defines the abstract syntax of the expressions package. This package defines the structure that OCL
expressions can have. An overview of the inheritance relationships between all classes defined in this package is shown
in Figure 12 on page 60.
ModelElement
(f rom Core)
- name : String
+type Classifier
+ body
1
+source
(from Core)
OclExpress ion
1
+initExpression
0..1
0..1
+type
1
+appliedProperty
0..1
PropertyCallExp
LiteralExp
IfExp
VariableExp
OclMessageExp
0..n
0..1
ModelPropertyCallExp
LoopExp
+loopExpr
+iterators 1..n
1 +referredVariable
VariableDeclaration 0..1
0..1
IteratorExp
varName : String
+result 1
IterateExp
+initalizedVariable
+baseExp
0..1
Figure 6 - The basic structure of the abstract syntax kernel metamodel for Expressions
8.3.1
Expressions Core
Figure 6 shows the core part of the Expressions package. The basic structure in the package consists of the classes
OclExpression, PropertyCallExp and VariableExp. An OclExpression always has a type, which is usually not
explicitly modeled, but derived. Each PropertyCallExp has exactly one source, identified by an OclExpression. In this
section we use the term ’property’, which is a generalization of Feature, AssociationEnd and predefined iterating OCL
collection operations.
40
A ModelPropertyCallExp generalizes all propertycalls that refer to Features or associations or AssociationEnds in
the UML metamodel. In Figure 9 on page 47 the various subtypes of ModelPropertyCallExp are defined.
Most of the remainder of the expressions package consists of a specification of the different subclasses of
PropertyCallExp and their specific structure. From the metamodel it can be deduced that an OCL expression always starts
with a variable or literal, on which a property is recusively applied.
IfExp
An IfExp is defined in Section 8.3.3 (“If Expressions”), but included in this diagram for completeness.
IterateExp
An IterateExp is an expression which evaluates its body expression for each element of a collection. It acts as a loop
construct that iterates over the elements of its source collection and results in a value. An iterate expression evaluates its
body expression for each element of its source collection. The evaluated value of the body expression in each iterationstep becomes the new value for the result variable for the succeding iteration-step. The result can be of any type and is
defined by the result association. The IterateExp is the most fundamental collection expression defined in the OCL
Expressions package.
Associations
•
result
The VariableDeclaration that represents the result variable.
IteratorExp
An IteratorExp is an expression which evaluates its body expression for each element of a collection. It acts as a loop
construct that iterates over the elements of its source collection and results in a value. The type of the iterator expression
depends on the name of the expression, and sometimes on the type of the associated source expression. The IteratorExp
represents all other predefined collection operations that use an iterator. This includes select, collect, reject, forAll, exists,
etc. The OCL Standard Library defines a number of predefined iterator expressions. Their semantics is defined in terms
of the iterate expression in , see Section 11.8, “Predefined Iterator Expressions,” on page 149.
LiteralExp
A LiteralExp is an expression with no arguments producing a value. In general the result value is identical with the
expression symbol. This includes things like the integer 1 or literal strings like ’this is a LiteralExp’.
LoopExp
A LoopExp is an expression that respresent a loop construct over a collection. It has an iterator variable that represents
the elements of the collection during iteration. The body expression is evaluated for each element in the collection. The
result of a loop expression depends on the specific kind and its name.
Associations
•
iterators
The VariableDeclarations that represents the iterator variables. These variables are,
each in its turn, bound to every element value of the source collection while evaluating
the body expression.
•
body
The OclExpression that is evaluated for each element in the source collection.
41
A ModelPropertyCall expression is an expression that refers to a property that is defined for a Classifier in the UML
model to which this expression is attached. Its result value is the evaluation of the corresponding property. In Section
8.3.2 (“Model PropertyCall Expressions”) the various subclasses of ModelPropertyCallExp are defined.
OclExpression
An OclExpression is an expression that can be evaluated in a given environment. OclExpression is the abstract
superclass of all other expressions in the metamodel. It is the top-level element of the OCL Expressions package. Every
OclExpression has a type that can be statically determined by analyzing the expression and its context. Evaluation of an
expression results in a value. Expressions with boolean result can be used as constraints, e.g. to specify an invariant of a
class. Expressions of any type can be used to specify queries, initial attribute values, target sets, etc..
The environment of an OclExpression defines what model elements are visible and can be referred to in an expression.
At the topmost level the environment will be defined by the ModelElement to which the OCL expression is attached, for
example by a Classifier if the OCL expression is used as an invariant. On a lower level, each iterator expression can also
introduce one or more iterator variables into the environment. the environment is not modeled as a separate metaclass,
because it can be completely derived using derivation rules. The complete derivation rules can be found in chapter 9
(“Concrete Syntax”).
Associations
•
appliedProperty
The property that is applied to the instance that results from evaluating this OclExpres-
sion.
•
type
The type of the value that is the result of evaluating the OclExpression.
•
parentOperation
The OperationCallExp where this OclExpression is an argument of. See Figure 9 on
page 47.
•
initializedVariable
The variable of which the result of this expression is the initial value.
OclMessageExp
OclMessageExp is defined in Section 8.3.4 (“Message Expressions”), but included in this diagram for completeness.
PropertyCallExp
A PropertyCallExp is an expression that refers to a property (operation, attribute, association end, predefined iterator for
collections). Its result value is the evaluation of the corresponding property. This is an abstract metaclass.
Associations
•
source
The result value of the source expression is the instance that performs the property call.
VariableDeclaration
A VariableDeclaration declares a variable name and binds it to a type. The variable can be used in expressions where
the variable is in scope. This metaclass represents amongst others the variables self and result and the variables defined
using the Let expression.
42
Associations
•
initExpression
The OclExpression that represents the initial value of the variable. Depending on the role
that a variable declaration plays, the init expression might be mandatory.
•
type
The Classifier which represents the type of the variable.
Attributes
•
varName
The String that is the name of the variable.
VariableExp
A VariableExp is an expression which consists of a reference to a variable. References to the variables self and result or
to variables defined by Let espressions are examples of such variable expressions.
Associations
•
referredVariable
The VariableDeclaration to which this variable expression refers. In the case of a self
expression the variable declaration is the definition of the self variable.
43
8.3.2
Model PropertyCall Expressions
A ModelPropertyCallExp can refer to any of the subtypes of Feature as defined in the UML kernel. This is shown in
Figure 9 by the three different subtypes, each of which is associated with its own type of ModelElement.
AttributeCallExp
0..n
+referredAttribute
1
Attribute
(from Core)
NavigationCallExp
+navigationSource
0..1
AssociationEndCallExp
0..n
AssociationClassCallExp
0..n
+qualifiers
{ordered} 0..n
{ordered} 0..n
+arguments
+parentOperation
0..1
0..n
OperationCallE xp
+referredAssociationEnd
1
1
AssociationEnd
(from Core)
+referredAssociationClass AssociationClass
(from Core)
1
OclExpression
1
Operation
(from Core)
+referredOperation
Figure 7 - Abstract syntax metamodel for ModelPropertyCallExp in the Expressions package
An AssociationEndCallExp is a reference to an AssociationEnd defined in a UML model. It is used to determine
objects linked to a target object by an association. The expression refers to these target objects by the role name of the
association end connected to the target class.
44
Associations
•
referredAssociationEnd
The AssociationEnd to which this AssociationEndCallExp is a reference. This refers
to an AssociationEnd of an Association that is defined in the UML model.
An AssociationClassCallExp is a reference to an AssociationClass defined in a UML model. It is used to determine
objects linked to a target object by an association class. The expression refers to these target objects by the name of the
target associationclass.
Associations
•
referredAssociationClass
The AssociationClass to which this AssociationClassCallExp is a reference. This
refers to an AssociationClass that is defined in the UML model.
AttributeCallExp
An AttributeCallExpression is a reference to an Attribute of a Classifier defined in a UML model. It evaluates to the
value of the attribute.
Associations
•
referredAttribute
The Attribute to which this AttributeCallExp is a reference.
NavigationCallExp
A NavigationCallExp is a reference to an AssociationEnd or an AssociationClass defined in a UML model. It is used
to determine objects linked to a target object by an association. If there is a qualifier attached to the source end of the
association then additional qualifiers expressions may be used to specify the values of the qualifying attributes.
Associations
•
qualifiers
The values for the qualifier attributes if applicable.
•
navigationSource
The source denotes the AssociationEnd at the end of the object itself. This is used to
resolve ambiguities when the same Classifier participates in more than one AssociationEnd in the same association. In other cases it can be derived.
OperationCallExp
A OperationCallExp refers to an operation defined in a Classifier. The expression may contain a list of argument
expressions if the operation is defined to have parameters. In this case, the number and types of the arguments must match
the parameters.
Associations
•
arguments
The arguments denote the arguments to the operation call. This is only useful when the
operation call is related to an Operation that takes parameters.
•
referredOperation
The Operation to which this OperationCallExp is a reference. This is an Operation of
a Classifier that is defined in the UML model.
45
8.3.3
If Expressions
This section describes the if expression in detail. Figure 8 shows the structure of the if expression.
IfExp
0..1
1
+thenExpression
0..1
0..1
1 +condition
OclExpression
1
+elseExpression
Figure 8 - Abstract syntax metamodel for if expression
IfExp
An IfExp results in one of two alternative expressions depending on the evaluated value of a condition. Note that both
the thenExpression and the elseExpression are mandatory. The reason behind this is that an if expression should always
result in a value, which cannot be guaranteed if the else part is left out.
Associations
•
condition
The OclExpression that represents the boolean condition. If this condition evaluates to
true, the result of the if expression is identical to the result of the thenExpression. If this
condition evaluates to false, the result of the if expression is identical to the result of the
elseExpression
•
thenExpression
The OclExpression that represents the then part of the if expression.
•
elseExpression
The OclExpression that represents the else part of the if expression.
8.3.4
Message Expressions
In the specification of communication between instances we unify the notions of asynchronous and synchronous
communication. The structure of the message expressions is shown in Figure 9.
OclMessageExp
An OclMessageExp is an expression that results in an collection of OclMessage value. An OclMessage is the
unification of a signal sent, and an operation call. The target of the operation call or signal sent is specified by the target
OclExpression. Arguments can be OclExpressions, but may also be unspecified value expressions for arguments whose
value is not specified. It covers both synchronous and asynchronous actions. See [Kleppe2000] for a complete description
and motivation of this type of expression, also called "action clause".
46
ModelElement
(from Core)
+type Classifier
UnspecifiedValueExp
1
+unspecified
(from Core)
0..1
0..1 OclMessageArg
OclExpression
{ordered}
+arguments
0..1
+expression 0..1
0..n
+target
OclMessageExp
1
+sentS igna l
0..1
SendAction
+calledOperation
0..1
CallAction
(from Common Behavior)
0..n
0..n
+operation
1
Operation
(from Core)
+signal
1
Signal
Figure 9 - The abstract syntax of Ocl messages
Associations
•
target
The OclExpression that represents the target instance to which the signal is sent.
•
arguments
The SignalArgs that represents the parameters to the Operation or Signal. The number
and type of arguments should conform to those defined in the Operation or Signal. The
order of the arguments is the same as the order of the parameters of the Operation or the
attributes of a Signal.
•
calledOperation
If this is a message to request an operation call, this is the requested CallAction.
•
sentSignal
If this is a UML signal sent, this is the SendAction.
47
OclMessageArg
An OclMessageArg is an argument of an OclMessageExp. It is either an OclExpression, or an UnspecifiedValueExp.
An OclExpression is used to specify the exact value of the parameter. An UnspecifiedValueExp is used when one does
not want, or is not able to specify the exact value of the parameter at the time of sending of the message. An
OclMessageArg has either a specified or an unspecified value.
Associations
•
expression
The OclExpression that represents an actual parameters to the Operation or Signal.
•
unspecified
The UnspecifiedValueExp that represents a random value that conforms to the type of this
expression.
UnspecifiedValueExp
An UnpecifiedValueExp is an expression whose value is unspecified in an OCL expression. It is used within OCL
messages to leave parameters of messages unspecified.
8.3.5
Literal Expressions
This section defines the different types of literal expressions of OCL. It also refers to enumeration types and enumeration
literals. Figure 10 shows all types of literal expressions.
BooleanLiteralExp
A BooleanLiteralExp represents the value true or false of the predefined type Boolean.
Attributes
•
booleanSymbol
The Boolean that represents the value of the literal.
CollectionItem
A CollectionItem represents an individual element of a collection.
CollectionKind
A CollectionKind is an enumeration of kinds of collections.
CollectionLiteralExp
A CollectionLiteralExp represents a reference to collection literal.
Attributes
•
kind
The kind of collection literal that is specified by this CollectionLiteralExp.
CollectionLiteralPart
A CollectionLiteralPart is a member of the collection literal.
Associations
•
48
type
The type of the collection literal.
LiteralExp
PrimitiveLiteralExp
NumericLiteralExp
TupleLiteralExp
+tuplePart 0..n
S tring Lite ra lE xp
stringSymbol : String
V ariab le Declaratio n
BooleanLiteralExp
booleanSymbol : Boolean
EnumLiteralExp
IntegerLiteralExp
RealLiteralExp
integerSymbol : Integer rea lS ymbo l : Rea l
Co llectionLiteralExp
kind : CollectionK ind
+parts
0..n {ordered}
+referredEnumLiteral 1
Enumeration 1
+lite ra l E numL iteral
(from Core)
(from Core)
+enumeration 0 ..n
Co llectio nRa nge
<<enumeration>>
Co llectio nKind
Collection
Set
Bag
Sequence
CollectionItem
0..1
0..1
1
+last
1
0..1
+first
+item
OclExpression
1
+type
1
Classifier
(fro m C ore )
Figure 10 - Abstract syntax metamodel for Literal expression
CollectionRange
A CollectionRange represents a range of integers.
EnumLiteralExp
An EnumLiteralExp represents a reference to an enumeration literal.
Associations
•
referredEnumLiteral
The EnumLiteral to which the enum expression refers.
IntegerLiteralExp
A IntegerLiteralExp denotes a value of the predefined type Integer.
49
Attributes
•
integerSymbol
The Integer that represents the value of the literal.
NumericLiteralExp
A NumericLiteralExp denotes a value of either the type Integer or the type Real.
PrimitiveLiteralExp
A PrimitiveLiteralExp literal denotes a value of a primitive type.
Attributes
•
symbol
The String that represents the value of the literal.
RealLiteralExp
A RealLiteralExp denotes a value of the predefined type Real.
Attributes
•
realSymbol
The Real that represents the value of the literal.
StringLiteralExp
A StringLiteralExp denotes a value of the predefined type String.
Attributes
•
stringSymbol
The String that represents the value of the literal.
TupleLiteralExp
A TupleLiteralExp denotes a tuple value. It contains a name and a value for each part of the tuple type.
8.3.6
Let expressions
This section defines the abstract syntax metamodel for Let expressions. The only addition to the abstract syntax is the
metaclass LetExp as shown in Figure 11. The other metaclasses are re-used from the previous diagrams.
Note that Let expressions that take arguments are no longer allowed in OCL 2.0. This feature is redundant. Instead, a
modeler can define an additional operation in the UML Classifier, potentially with a special stereotype to denote that this
operation is only ment to be used as a helper operation in OCL expressions. The postcondition of such an additional
operation can then define its result value. Removal of Let functions will therefore not affect the expressibility of the
modeler. Another way to define such helper operations is through the <<definition>> constraint, which reuses some of the
concrete syntax defined for Let expressions (see Section 12.5, “Definition,” on page 157), but is nothing more than an
OCL-based syntax for defining helper attributes and operations.
LetExp
A LetExp is a special expression that defined a new variable with an initial value. A variable defined by a LetExp cannot
change its value. The value is always the evaluated value of the initial expression. The variable is visible in the in
expression.
50
+in
OclExpression +initExpression
0 ..1
1
0..1
0..1
+va riable
LetExp
0..1
1
+initalizedVariable
VariableDeclaration
varName : String
Figure 11 - Abstract syntax metamodel for let expression
Associations
•
variable
The VariableDeclaration that defined the variable.
•
in
The OclExpression in whose environment the defined variable is visible.
8.3.7
Well-formedness Rules of the Expressions package
The metaclasses defined in the abstract syntax have the following well-formednes rules:
AttributeCallExp
The type of the Attribute call expression is the type of the referred attribute.
context AttrubuteCallExp
inv: type = referredAttribute.type
BooleanLiteralExp
[1] The type of a boolean Literal expression is the type Boolean.
context BooleanLiteralExp
inv: self.type.name = ’Boolean’
CollectionLiteralExp
[1] ’Collection’ is an abstract class on the M1 level and has no M0 instances.
context CollectionLiteralExp
inv: kind <> CollectionKind::Collection
[2] The type of a collection literal expression is determined by the collection kind selection and the common supertype of all
elements. Note that the definition below implicitly states that empty collections have OclVoid as their elementType.
context CollectionLiteralExp
inv: kind = CollectionKind::Set
implies type.oclIsKindOf (SetType )
inv: kind = CollectionKind::Sequence implies type.oclIsKindOf (SequenceType)
inv: kind = CollectionKind::Bag
implies type.oclIsKindOf (BagType )
51
inv: type.oclAsType (CollectionType).elementType = parts->iterate (p; c : Classifier = OclVoid | c.commonSuperType (p.type))
No additional well-formedness rules.
CollectionItem
[1] The type of a CollectionItem is the type of the item expression.
context CollectionItem
inv: type = item.type
CollectionRange
[1] The type of a CollectionRange is the common supertype of the expressions taking part in the range.
context CollectionRange
inv: type = first.type.commonSuperType (last.type)
EnumLiteralExp
[1] The type of an enum Literal expression is the type of the referred literal.
context EnumLiteralExp
inv: self.type = referredEnumLiteral.enumeration
IfExp
[1] The type of the condition of an if expression must be Boolean.
context IfExp
inv: self.condition.type.oclIsKindOf(Primitive) and self.condition.type.name = ’Boolean’
[2] The type of the if expression is the most common supertype of the else and then expressions.
context IfExp
inv: self.type = thenExpression.type.commonSuperType(elseExpression.type)
IntegerLiteralExp
[1] The type of an integer Literal expression is the type Integer.
context IntegerLiteralExp
inv: self.type.name = ’Integer’
IteratorExp
[1] If the iterator is ’forAll’, ’isUnique’, or ’exists’ the type of the iterator must be Boolean.
context IteratorExp
inv: name = ’exists’ or name = ’forAll’ or name = ’isUnique’
implies type.oclIsKindOf(Primitive) and type.name = ’Boolean’
[2] The result type of the collect operation on a sequence type is a sequence, the result type of ’collect’ on any other collection type is a Bag. The type of the body is always the type of the elements in the return collection.
context IteratorExp
inv: name = ’collect’ implies
if source.type.oclIsKindOf(SequenceType) then
type = expression.type.collectionType->select(oclIsTypeOf(SequenceType))->first()
else
type = expression.type.collectionType->select(oclIsTypeOf(BagType))->first()
52
endif
[3] The ’select’and ’reject’ iterators have the same type as its source.
context IteratorExp
inv: name = ’select’ or name = ’reject’ implies type = source.type
[4] The type of the body of the select, reject,exists and forAll must be boolean.
context IteratorExp
inv: name = ’exists’ or name = ’forAll’ or name = ’select’ or name = ’reject’
implies body.type.name = ’Boolean’
IterateExp
[1] The type of the iterate is the type of the result variable.
context IterateExp
inv: type = result.type
[2] The type of the body expression must conform to the declared type of the result variable.
context IterateExp
body.type.conformsTo(result.type)
[3] A result variable must have an init expression.
context IterateExp
inv: self.result.initExpression->size() = 1
LetExp
[1] The type of a Let expression is the type of the in expression.
context LetExp
inv: type = in.type
LiteralExp
LoopExp
[1] The type of the source expression must be a collection.
context LoopExp
inv: source.type.oclIsKindOf (CollectionType)
[2] The loop variable of an iterator expression has no init expression.
context LoopExp
inv: self.iterators->forAll(initExpression->isEmpty())
[3] The type of each iterator variable must be the type of the elements of the source collection.
context IteratorExp
inv: self.iterators->forAll(type = source.type.oclAsType (CollectionType).elementType)
53
NumericLiteralExp
OclExpression
OclMessageArg
[1] There is either an expression or an unspecified value.
context OclMessageArg
inv: expression->size() + unspecified->size() = 1
OclMessageExp
[1] If the message is a call action, the arguments must conform to the parameters of the operation.
context OclMessageExp
inv: calledOperation->notEmpty() implies
arguments->forall (a | a.getType().conformsTo
(self.calledOperation.operation.parameter->
select( kind = ParameterDirectionKind::in )
->at (arguments->indexOf (a)).type))
[2] If the message is a send action, the arguments must conform to the attributes of the signal.
inv: sentSignal->notEmpty() implies
arguments->forall (a | a.getType().conformsTo
(self.sentSignal.signal.feature.oclAsType(StructuralFeature) )
->at (arguments->indexOf (a)).type))
[3] If the message is a call action, the operation must be an operation of the type of the target expression.
inv: calledOperation->notEmpty() implies
target.type.allOperations()->includes(calledOperation.operation)
[4] An OCL message has either a called operation or a sent signal.
inv: calledOperation->size() + sentMessage->size() = 1
[5] The target of an OCL message cannot be a collection.
inv: not target.type.oclIsKindOf (CollectionType)
OperationCallExp
[1] All the arguments must conform to the parameters of the referred operation
context OperationCallExp
inv: arguments->forall (a | a.type.conformsTo
(self.refParams->at (arguments->indexOf (a)).type))
[2] There must be exactly as many arguments as the referred operation has parameters.
inv: arguments->size() = refParams->size()
[3] An additional attribute refParams lists all parameters of the referred operation except the return and out parameter(s).
54
def: refParams: Sequence(Parameter) = referredOperation.parameters->select (p |
p.kind <> ParameterDirectionKind::return or
p.kind <> ParameterDirectionKind::out)
PropertyCallExp
RealLiteralExp
[1] The type of a real Literal expression is the type Real.
context RealLiteralExp
inv: self.type.name = ’Real’
StringLiteralExp
[1] The type of a string Literal expression is the type String.
context StringLiteralExp
inv: self.type.name = ’String’
TupleLiteralExp
[1] The type of a TupleLiteralExp is a TupleType with the specified parts.
context TupleLiteralExp
inv: type.oclIsKindOf (TupleType)
and
tuplePart->forAll (tlep |
type.oclAsType (TupleType).allAttributes()->exists (tp | tlep.attribute = tp))
and
tuplePart->size() = type.oclAsType (TupleType).allAttributes()->size()
[2] All tuple literal expression parts of one tuple literal expression have unique names.
context TupleLiteralExp
inv: tuplePart->isUnique (attribute.name)
TupleLiteralExpPart
[1] The type of the attribute is the type of the value expression.
context TupleLiteralExpPart
inv: attribute.type = value.type
UnspecifiedValueExp
VariableDeclaration
[1] For initialized variable declarations, the type of the initExpression must conform to the type of the declared variable.
context VariableDeclaration
inv: initExpression->notEmpty() implies initExpression.type.conformsTo (type)
VariableExp
[1] The type of a VariableExp is the type of the variable to which it refers.
55
context VariableExp
inv: type = referredVariable.type
8.3.8
Additional Operations on UML metaclasses
In the chapters “Abstract Syntax,” “Concrete Syntax,” “The Use of Ocl Expressions in UML Models,” and appendix
“Semantics Described using UML” many additional operations on UML metaclasses are used. They are defined in this
section. The next section defines additional operations for the OCL metaclasses
Classifier
The operation commonSuperType results in the most specific common supertype of two classifiers.
context Classifier
def: commonSuperType (c : Classifier) : Classifier =
Classifier.allInstances()->select (cst |
c.conformsTo (cst) and
self.conformsTo (cst) and
not Classifier.allInstances()->exists (clst |
c.conformsTo (clst) and
self.conformsTo (clst) and
clst.conformsTo (cst) and
clst <> cst
)
)->any (true)
The following operations have been added to Classifier to lookup attributes, associationEnds and operations.
context Classifier
def: lookupAttribute(attName : String) : Attribute =
self.allAttributes->any(me | me.name = attName)
def: lookupAssociationEnd(name : String) : AssociationEnd =
self.allAssociationEnds->any (ae | ae.name = name)
def: lookupAssociationClass(name : String) : AssociationClass =
self.allAssociationClasses->any (ae | ae.name = name)
def: lookupOperation (name: String, paramTypes: Sequence(Classifier)): Operation =
self.allOperations->any (op | op.name = name and
op.hasMatchingSignature(paramTypes))
def: lookupSignal (sigName: String, paramTypes: Sequence(Classifier)): Operation =
self.allReceptions.signal->any (sig | sig.name = sigName and
sig.hasMatchingSignature(paramTypes))
Operations allAttributes, allOperations, etc. are defined in the UML semantics. The operation allReceptions is missing
and defined here. The operation allReceptions results in a Set containing all Signals that the Classifier has as Receptions
itself and all its inherited Attributes.
context Classifier
def: allReceptions : set(Reception) =
self.allFeatures->select(f | f.oclIsKindOf(Reception))
Operation
An additional operation is added to Operation, which checks whether its signature matches with a sequence of Clasifiers.
Note that in making the match only parameters with direction kind ‘in’ are considered.
56
context Operation
def: hasMatchingSignature(paramTypes: Sequence(Classifier)) : Boolean =
-- check that operation op has a signature that matches the given parameter lists
= let sigParamTypes: Sequence(Classifier) = self.allAttributes.type in
(
( sigParamTypes->size() = paramTypes->size() ) and
( Set{1..paramTypes->size()}->forAll ( i |
paramTypes->at (i).conformsTo (sigParamTypes->at (i))
)
)
)
Parameter
The operation asAttribute results in an attribute that has the same name, type, etc. as the parameter.
context Parameter::asAttribute(): Attribute
pre: -- none
post: result.name
= self.name
post: result.type
= self.type
post: result.multiplicity
=1
post: result.targetscope
= ScopeKind::instance
post: result.ownerscope
post: result.ordering
= OrderingKind::unordered
post: result.visibility
= VisibilityKind::private
post: result.stereotype.name
= ’OclHelper’
An additional class operation is added to Parameter to return a Parameter.
context Parameter::make(n : String, c : Classifier, k : ParameterDirectionKind) :Parameter
post: result.name = n
post: result.kind = k
post: result.type = c
post: result.stereotype.name = ’OclHelper’
Signal
An additional operation is added to Signal, which checks whether its signature matches with a sequence of Clasifiers.
Note that in making the match the parameters of the signal are its attributes.
context Signal
def: hasMatchingSignature(paramTypes: Sequence(Classifier)) : Boolean =
-- check that signal has a signature that matches the given parameter lists
= let opParamTypes: Sequence(Classifier) = self.parameter->select (p | p.kind <>
ParameterDirectionKind::return).type in
(
( opParamTypes->size() = paramTypes->size() ) and
( Set{1..paramTypes->size()}->forAll ( i |
paramTypes->at (i).conformsTo (opParamTypes->at (i))
)
)
)
State
The operation getStateMachine() returns the statemachine to which a state belongs.
57
context State::getStateMachine() : StateMachine
post: result =
if statemachine->notEmpty() then
stateMachine
else
-- must be part of a composite state
state.container.getStateMachine()
endif
Transition
The operation getStateMachine() returns the statemachine to which a transition belongs.
context Transition::getStateMachine() : StateMachine
post: result =
if statemachine->notEmpty() then
stateMachine
else
-- state is not empty
state.getStateMachine()
endif
8.3.9
Additional Operations on OCL metaclasses
In chapters “Abstract Syntax,” “Concrete Syntax,” “The Use of Ocl Expressions in UML Models,” and appendix
“Semantics Described using UML” many additional operations on OCL metaclasses are used. They are defined in this
section. The previous section defines additional operations for the UML metaclasses
OclExpression
The following operation returns an operation call expression for the predefined atPre() operation with the self expression
as its source.
OclExpression::withAtPre() : OperationCallExp
post: result.name = ’atPre’
post: result.arguments->isEmpty()
post: result.source = self
The following operation returns an operation call expression for the predefined asSet() operation with the self expression
as its source.
OclExpression::withAsSet() : OperationCallExp
post: result.name = ’asSet’
post: result.arguments->isEmpty()
post: result.source = self
OclMessageArg
An additional operation is added to oclMessageArg to return the type of the argument.
context OclMessageArg
def: getType() : Classifier = if unspecified->notEmpty()
then unspecified.type
else expression.type
endif
58
TupleType
An additional class operation is added to Tuple to return a new tuple. The name of a tupletype is defined in the abstract
syntax chapter and need not to be specified here.
context TupleType::make(atts : sequence(Attribute) ) : TupleType
post: result.features = atts
post: result.stereotype.name = ’OclHelper’
VariableDeclaration
An additional operation is added to VariableDeclaration to return a corresponding Parameter.
context VariableDeclaration::asParameter() : Parameter
post: result.name = self.varName
post: result.kind = ParameterKind::in
post: result.type = self.type
An additional operation is added to VariableDeclaration to return a corresponding Attribute.
context VariableDeclaration::asAttribute() : Attribute
post: result.name
= self.varName
post: result.type
= self.type
post: result.multiplicity
=1
post: result.targetscope
post: result.ownerscope
post: result.ordering
= OrderingKind::unordered
post: result.visibility
= VisibilityKind::private
post: result.constraint.bodyExpression = self.initExpression
post: result.stereotype.name
= ’OclHelper’
59
8.3.10 Overview of class hierarchy of OCL Abstract Syntax metamodel
M odelEl em ent
(f rom Core)
<<enumerat ion>>
CollectionKind
VariableDeclaration
UnspecifiedValueExp
CollectionItem
OclMessageArg
CollectionRange
Ocl Expres si on
VariableExp
IfExp
LiteralExp
PropertyCallExp
LetExp
OclMessageExp
LoopExp
Col lecti onLiteral Exp
TupleLiteralExp
Prim it iveLiteralE xp
OperationCallExp
IteratorExp
BooleanLiteralExp
StringLiteralExp
Model PropertyCal lExp
EnumLiteralExp
AttributeCallExp
IterateExp
NavigationCallExp
NumericLiteralExp
IntegerLiteralExp
RealLiteralExp
Figure 12 - Overview of the abstract syntax metamodel for Expressions
60
9
Concrete Syntax
This section describes the concrete syntax of the OCL. This allows modelers to write down OCL expressions in a
standardized way. A formal mapping from the concrete syntax to the abstract syntax from Chapter 8 (“Abstract Syntax”)
is given. Although not required by the UML 2.0 for OCL RFP, Section 9.6 describes a mapping from the abstract syntax
to the concrete syntax. This allows one to produce a standard human readable version of any OCL expression that is
represented as an instance of the abstract syntax.
Section 9.1 (“Structure of the Concrete Syntax”) describes the structure of the grammar and the motivation for the use of
an attribute grammar.
9.1
Structure of the Concrete Syntax
The concrete syntax of OCL is described in the form of an a full attribute grammar. Each production in an attribute
grammar may have synthesized attributes attached to it. The value of synthesized attributes of elements on the left hand
side of a production rule is always derived from attributes of elements at the right hand side of that production rule. Each
production may also have inherited attributes attached to it. The value of inherited attributes of elements on the right
hand side of a production rule is always derived from attributes of elements on the left hand side of that production.
In the attribute grammar that specifies the concrete syntax, every production rule is denoted using the EBNF formalism
and annotated with synthesised and inherited attributes, and disambiguating rules. There are a number of special
annotations:
Synthesized attributes. Each production rule has one synthesized attribute called ast (short for abstract syntax tree),
that holds the instance of the OCL Abstract Syntax that is returned by the rule. The type of ast is different for every rule,
but it always is an element of the abstract syntax. The type is stated with each production rule under the heading "Abstract
Syntax Mapping". The ast attribute constitutes the formal mapping from concrete syntax to abstract syntax.
The motivation for the use of an attribute grammar is the easiness of the construction and the clarity of this mapping.
Note that each name in the EBNF format of the production rule is postfixed with ’CS’ to clearly distinguish between the
concrete syntax elements and their abstract syntax counterparts.
Inherited attributes. Each production rule has one inherited attribute called env (short for environment), that holds a
list of names that are visible from the expression. All names are references to elements in the model. In fact, env is a
name space environment for the expression or expression part denoted according to the production rule. The type of the
env attribute is Environment, as shown in Figure 13 on page 62. A number of operations are defined for this type. Their
definitions and more details on the Environment type can be found in Section 9.4 (“Environment definition”). The manner
in which both the ast and env attributes are determined, is given using OCL expressions.
Note that the contents of the env attribute are fully determined by the context of the OCL expression. When an OCL
expression is used as an invariant to class X, its environment will be different than in the case the expression is used as a
postcondition to an operation of class Y. In Chapter 12 (“The Use of Ocl Expressions in UML Models”) the context of
OCL expressions is defined in detail.
Multiple production rules. For some elements there is a choice of multiple production rules. In that case the EBNF
format of each production rule is prefixed by a capital letter between square brackets. The same prefix is used for the
corresponding determination rules for the ast and env attributes.
61
E nvironm ent
EMPTY_ENV : Environment
lookupLocal()
lookup()
lookupLocal()
lookup()
addElement()
addNamespace()
nestedEnvironment()
lookupImplicitAttribute()
lookupImplicitSourceForAttribute()
lookupImplicitAssociationEnd()
lookupImplicitOperation()
+namedElements
0..n
NamedElement
name : String
mayBeImplicit : Boolean
+referredElement
1
M od elElem ent
(from Core)
getType()
Figure 13 - The Environment type
Multiple occurences of production names. In some production rules the same element name is used more than once.
To distinguish between these occurences the names will be postfixed by a number in square brackets, as in the following
example.
CollectionRangeCS ::= OclExpressionCS[1] ’..’ OclExpressionCS[2]
Disambiguating rules. Some of the production rules are syntactically ambiguous. For such productions disambiguating
rules have been defined. Using these rules, each production and thus the complete grammar becomes nonambiguous. For
example in parsing a.b(), there are at least three possible parsing solutions:
1.
a is a VariableExpr
(a reference to a let or an iterator variable)
2.
a is an AttributeCallExp
(self is implicit)
3.
a is a NavigationCallExp (self is implicit)
A decision on which grammar production rule to use, can only be made when the environment of the expression is taken
into account. The disambiguating rules describe these choices based on the environment and allow unambiguous parsing
of a.b(). In this case the rules (in plain English) would be:
• If a is a defined variable in the current scope, a is a VariableExp.
• If not, check self and all iterator variables in scope. The inner-most scope for which as is either
62
• an attribute with the name a, resulting in an AttributeCallExp,
• or an opposite association-end with the name a, resulting in a NavigationCallExp,
• defines the meaning of a.b().
• If neither of the above is true, the expression is illegal / incorrect and cannot be parsed.
Disambiguating rules may be based on the UML model to which the OCL expresion is attached (e.g does an attribute
exist or not). Because of this, the UML model must be available when an OCL expression is parsed, otherwise it cannot
be validated as a correct expression. The grammar is structured in such a way that at most one of the production rules will
fullfil all the disambiguating rules, thus ensuring that the grammar as a whole is unambiguous. The disambiguating rules
are written in OCL, and use some metaclasses and additional operations from the UML 1.4 semantics.
9.2
A Note to Tool Builders
9.2.1
Parsing
The grammar in this chapter might not prove to be the most efficient way to directly construct a tool. Of course, a toolbuilder is free to use a different parsing mechnism. He can e.g. first parse an OCL expression using a special concrete
syntax tree, and do the semantic validation against a UML model in a second pass. Also, error correction or syntax
directed editing might need hand-optimized grammars. This document does not prescribe any specific parsing approach.
The only restriction is that at the end of all processing a tool should be able to produce the same well-formed instance of
the abstract syntax, as would be produced by this grammar.
9.2.2
Visibility
The OCL specification puts no restrictions on visibility. In OCL, all modelelements are considered visible. The reason for
this is to allow a modeler to specify constraints, even between ‘hidden’ elements. At the lowest implementation level this
might be useful.
As a separate option OCL tools may enforce all UML visibility rules to support OCL expressions to be specified only
over visible modelelements. Especially when a tool needs to generate code for runtime evaluation of OCL expressions,
this visibility enforcement is necessary.
9.3
Concrete Syntax
ExpressionInOclCS
The ExpressionInOcl symbol has been added to setup the initial environment of an expression.
ExpressionInOclCS ::= OclExpressionCS
Abstract syntax mapping
ExpressionInOclCS.ast : OclExpression
Synthesized attributes
ExpressionInOclCS.ast = OclExpressionCS.ast
63
Inherited attributes
The environment of the OCL expression must be defined, but what exactly needs to be in the environment depends on the
context of the OCL expression. The following rule is therefore not complete. It defines the env attribute by adding the self
variable to an empty environment, as well as a Namespace containing all elements visible from self. (In Section 12.2,
“The ExpressionInOcl Type,” on page 155 the contextualClassifier will be defined for the various places where an ocl
expression may occur.) In the context of a pre- or postcondition, the result variable as well as variable definitions for any
named operation parameters can be added in a similar way.
OclExpressionCS.env =
ExpressionInOclCS.contextualClassifier.namespace.getEnvironmentWithParents()
.addElement (’self’, ExpressionInOclCS.contextualClassifier, true)
OclExpressionCS
An OclExpression has several production rules, one for each subclass of OclExpression. Note that UnspecifiedValueExp
is handled explicitly in OclMessageArgCS, because that is the only place where it is allowed.
[A] OclExpressionCS ::= PropertyCallExpCS
[B] OclExpressionCS ::= VariableExpCS
[C] OclExpressionCS ::= LiteralExpCS
[D] OclExpressionCS ::= LetExpCS
[E] OclExpressionCS ::= OclMessageExpCS
[F] OclExpressionCS ::= IfExpCS
OclExpressionCS.ast : OclExpression
[A] OclExpressionCS.ast = PropertyCallExpCS.ast
[B] OclExpressionCS.ast = VariableExpCS.ast
[C] OclExpressionCS.ast = LiteralExpCS.ast
[D] OclExpressionCS.ast = LetExpCS.ast
[E] OclExpressionCS.ast = OclMessageExpCS.ast
[F] OclExpressionCS.ast = IfExpCS.ast
[A] PropertyCallExpCS.env = OclExpressionCS.env
[B] VariableExpCS.env
= OclExpressionCS.env
[C] LiteralExpCS.env
[D] LetExpCS.env
[E] OclMessageExpCS.env = OclExpressionCS.env
[F] IfExpCS.env
Disambiguating rules
The disambiguating rules are defined in the children.
VariableExpCS
A variable expression is just a name that refers to a variable.
VariableExpCS ::= simpleNameCS
64
VariableExpCS.ast : VariableExpression
VariableExpCS.ast.referredVariable =
env.lookup(simpleNameCS.ast).referredElement.oclAsType(VariableDeclaration)
-- none
[1] simpleName must be a name of a visible VariableDeclaration in the current environment.
env.lookup (simpleNameCS.ast).referredElement.oclIsKindOf (VariableDeclaration)
simpleNameCS
This production rule represents a single name. No special rules are applicable. The exact syntax of a String is undefined
in UML 1.4, and remains undefined in OCL 2.0. The reason for this is internationalization.
simpleNameCS ::= <String>
simpleNameGr.ast : String
simpleNameGr.ast = <String>
-- none
-- none
pathNameCS
This rule represents a path name, which is held in its ast as a sequence of Strings.
pathNameCS ::= simpleNameCS (’::’ pathNameCS )?
pathNameCS.ast : Sequence(String)
pathNameCS.ast = Sequence{simpleNameCS.ast}->union(pathNameCS.ast)
-- none
65
-- none
LiteralExpCS
This rule represents literal expressions.
[A] LiteralExpCS ::= EnumLiteralExpCS
[B] LiteralExpCS ::= CollectionLiteralExpCS
[C] LiteralExpCS ::= TupleLiteralExpCS
[D] LiteralExpCS ::= PrimitiveLiteralExpCS
LiteralExpCS.ast : LiteralExp
[A] LiteralExpCS.ast = EnumLiteralExpCS.ast
[B] LiteralExpCS.ast = CollectionLiteralExpCS.ast
[C] LiteralExpCS.ast = TupleLiteralExpCS.ast
[D] LiteralExpCS.ast = PrimitiveLiteralExpCS.ast
[A] EnumLiteralExpCS.env
= LiteralExpCS.env
[B] CollectionLiteralExpCS.env = LiteralExpCS.env
[C] TupleLiteralExpCS.env = LiteralExpCS.env
[D] PrimitiveLiteralExpCS.env = LiteralExpCS.env
-- none
EnumLiteralExpCS
The rule represents Enumeration Literal expressions.
EnumLiteralExpCS ::= pathNameCS ’::’ simpleNameCS
EnumLiteralExpCS.ast : EnumLiteralExp
EnumLiteralExpCS.ast.type =
env.lookupPathName (pathNameCS.ast).referredElement.oclAsType (Classifier)
EnumLiteralExpCS.ast.referredEnumLiteral =
EnumLiteralExpCS.ast.type.oclAsType (Enumeration).literal->
select (l | l.name = simpleNameCS.ast )->any(true)
-- none
[1] The specified name must indeed reference an enumeration:
66
not EnumLiteralExpCS.ast.type.oclIsUndefined() and
EnumLiteralExpCS.ast.type.oclIsKindOf (Enumeration)
CollectionLiteralExpCS
This rule represents a collection literal expression.
CollectionLiteralExpCS ::= CollectionTypeIdentifierCS
‘{‘ CollectionLiteralPartsCS? ‘}’
CollectionLiteralExpCS.ast : CollectionLiteralExp
CollectionLiteralExpCS.ast.parts = CollectionLiteralPartsCS.ast
CollectionLiteralExpCS.ast.kind = CollectionTypeIdentifierCS.ast
CollectionTypeIdentifierCS.env = CollectionLiteralExpCS.env
CollectionLiteralPartsCS.env = CollectionLiteralExpCS.env
[1] In a literal the collectiuon type may not be Collection
CollectionTypeIdentifierCS.ast <> ’Collection’
CollectionTypeIdentifierCS
This rule represent the type indentifier in a collection literal expression. The Collection type is an abstract type on M1
level, so it has no corresponding literals.
[A] CollectionTypeIdentifierCS ::= ’Set’
[B] CollectionTypeIdentifierCS ::= ’Bag’
[C] CollectionTypeIdentifierCS ::= ’Sequence’
[D] CollectionTypeIdentifierCS ::= ’Collection’
[E] CollectionTypeIdentifierCS ::= ’OrderedSet’
CollectionTypeIdentifierCS.ast : CollectionKind
[A] CollectionTypeIdentifierCS.ast = CollectionKind::Set
[B] CollectionTypeIdentifierCS.ast = CollectionKind::Bag
[C] CollectionTypeIdentifierCS.ast = CollectionKind::Sequence
[D] CollectionTypeIdentifierCS.ast = CollectionKind::Collection
[E] CollectionTypeIdentifierCS.ast = CollectionKind::OrderedSet
-- none
67
-- none
CollectionLiteralPartsCS
This production rule describes a sequence of items that are the contents of a collection literal.
CollectionLiteralPartsCS[1] = CollectionLiteralPartCS
( ’,’ CollectionLiteralPartsCS[2] )?
CollectionLiteralPartsCS[1].ast : Sequence(CollectionLiteralPart)
CollectionLiteralPartsCS[1].ast =
Sequence{CollectionLiteralPartCS.ast}->union(CollectionLiteralPartsCS[2].ast)
CollectionLiteralPartCS.env = CollectionLiteralPartsCS[1].env
CollectionLiteralPartSCS[2].env = CollectionLiteralPartsCS[1].env
-- none
CollectionLiteralPartCS
[A] CollectionLiteralPartCS ::= CollectionRangeCS
[B] CollectionLiteralPartCS ::= OclExpressionCS
CollectionLiteralPartCS.ast : CollectionLiteralPart
[A] CollectionLiteralPartCS.ast = CollectionRange.ast
[B] CollectionLiteralPartCS.ast.oclIsKindOf(CollectionItem) and
CollectionLiteralPartCS.ast.oclAsType(CollectionItem).OclExpression =
OclExpressionCS.ast
[A] CollectionRangeCS.env = CollectionLiteralPartCS.env
[B] OclExpressionCS.env = CollectionLiteralPartCS.env
-- none
CollectionRangeCS
CollectionRangeCS ::= OclExpressionCS[1] ’..’ OclExpressionCS[2]
68
CollectionRangeCS.ast : CollectionRange
CollectionRangeCS.ast.first = OclExpressionCS[1].ast
CollectionRangeCS.ast.last = OclExpressionCS[2].ast
OclExpressionCS[1].env = CollectionRangeCS.env
OclExpressionCS[2].env = CollectionRangeCS.env
-- none
PrimitiveLiteralExpCS
This includes Real, Boolean, Integer and String literals. Exprecially String literals must take internationalisation into
account and might need to remain undefined in this specification.
[A] PrimitiveLiteralExpCS ::= IntegerLiteralExpCS
[B] PrimitiveLiteralExpCS ::= RealLiteralExpCS
[C] PrimitiveLiteralExpCS ::= StringLiteralExpCS
[D] PrimitiveLiteralExpCS ::= BooleanLiteralExpCS
PrimitiveLiteralExpCS.ast : PrimitiveLiteralExp
[A] PrimitiveLiteralExpCS.ast = IntegerLiteralExpCS.ast
[B] PrimitiveLiteralExpCS.ast = RealLiteralExpCS.ast
[C] PrimitiveLiteralExpCS.ast = StringLiteralExpCS.ast
[D] PrimitiveLiteralExpCS.ast = BooleanLiteralExpCS.ast
-- none
-- none
TupleLiteralExpCS
This rule represents tuple literal expressions.
TupleLiteralExpCS ::= ‘Tuple’ ‘{‘ variableDeclarationListCS ‘}’
TupleLiteralExpCS.ast : TupleLiteralExp
TupleLiteralExpCS.tuplePart = variableDeclarationListCS.ast
69
variableDeclarationListCS[1].env = TupleLiteralExpCS.env
[1] The initExpression and type of all VariableDeclarations must exist.
TupleLiteralExpCS.tuplePart->forAll( varDecl |
varDecl.initExpression->notEmpty() and not varDecl.type.oclIsUndefined() )
IntegerLiteralExpCS
This rule represents integer literal expressions.
IntegerLiteralExpCS ::= <String>
IntegerLiteralExpCS.ast : IntegerLiteralExp
IntegerLiteralExpCS.ast.integerSymbol = <String>.toInteger()
-- none
-- none
RealLiteralExpCS
This rule represents real literal expressions.
RealLiteralExpCS ::= <String>
RealLiteralExpCS.ast : RealLiteralExp
RealLiteralExpCS.ast.realSymbol = <String>.toReal()
-- none
-- none
StringLiteralExpCS
This rule represents string literal expressions.
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StringLiteralExpCS ::= ’’’ <String> ’’’
StringLiteralExpCS.ast : StringLiteralExp
StringLiteralExpCS.ast.symbol = <String>
-- none
-- none
BooleanLiteralExpCS
This rule represents boolean literal expressions.
[A] BooleanLiteralExpCS ::= ’true’
[B] BooleanLiteralExpCS ::= ’false’
BooleanLiteralExpCS.ast : BooleanLiteralExp
[A] BooleanLiteralExpCS.ast.booleanSymbol = true
[B] BooleanLiteralExpCS.ast.booleanSymbol = false
-- none
-- none
PropertyCallExpCS
This rule represents property call expressions.
[A] PropertyCallExpCS ::= ModelPropertyCallExpCS
[B] PropertyCallExpCS ::= LoopExpCS
PropertyCallExpCS.ast : PropertyCallExp
[A] PropertyCallExpCS.ast = ModelPropertyCallCS.ast
[B] PropertyCallExpCS.ast = LoopExpCS.ast
[A] ModelPropertyCallCS.env = PropertyCallExpCS.env
71
[B] LoopExpCS.env
= PropertyCallExpCS.env
The disambiguating rules are defined in the children.
LoopExpCS
This rule represents loop expressions.
[A] LoopExpCS ::= IteratorExpCS
[B] LoopExpCS ::= IterateExpCS
LoopExpCS.ast : LoopExp
[A] LoopExpCS.ast = IteratorExpCS.ast
[B] LoopExpCS.ast = IterateExpCS.ast
[A] IteratorExpCS.env = LoopExpCS.env
[B] IterateExpCS.env = LoopExpCS.env
-- none
IteratorExpCS
The first alternative is a straightforward Iterator expression, with optional iterator variable. The second and third
alternatives are so-called implicit collect iterators. B is for operations and C for attributes, D for navigations and E for
associationclasses.
[A] IteratorExpCS ::= OclExpressionCS[1] ’->’ simpleNameCS
’(’ (VariableDeclarationCS[1],
(’,’ VariableDeclarationCS[2])? ’|’ )?
OclExpressionCS[2]
’)’
[B] IteratorExpCS ::= OclExpressionCS ’.’ simpleNameCS ’(’argumentsCS?’)’
[C] IteratorExpCS ::= OclExpressionCS ’.’ simpleNameCS
[D] IteratorExpCS ::= OclExpressionCS ’.’ simpleNameCS
(’[’ argumentsCS ’]’)?
[E] IteratorExpCS ::= OclExpressionCS ’.’ simpleNameCS
(’[’ argumentsCS ’]’)?
IteratorExpCS.ast : IteratorExp
-- the ast needs to be determined bit by bit, first the source association of IteratorExp
[A] IteratorExpCS.ast.source
= OclExpressionCS[1].ast
72
-- next the iterator association of IteratorExp
-- when the variable declaration is present, its ast is the iterator of this iteratorExp
-- when the variable declaration is not present, the iterator has a default name and
-- type
-- In any case, the iterator does not have an init expression
[A] IteratorExpCS.ast.iterators->at(1).name = if VariableDeclarationCS[1]->isEmpty()
then ’’
else VariableDeclarationCS[1].ast.name
endif
[A] IteratorExpCS.ast.iterator->at(1).type =
if VariableDeclarationCS[1]->isEmpty() or
(VariableDeclarationCS[1]->notEmpty() and
VariableDeclarationCS[1].ast.type.oclIsUndefined() )
then
OclExpressionCS[1].type.oclAsType (CollectionType).elementType
else
VariableDeclarationCS[1].ast.type
endif
- The optional second iterator
[A] if VariableDeclarationCS[2]->isEmpty() then
IteratorExpCS.ast.iterators->size() = 1
else
IteratorExpCS.ast.iterators->at(2).name = VariableDeclarationCS[2].ast.name
and
IteratorExpCS.ast.iterators->at(2).type =
then
else
endif
endif
[A] IteratorExpCS.ast.iterators->forAll(initExpression->isEmpty())
-- next the name attribute and body association of the IteratorExp
[A] IteratorExpCS.ast.name = simpleNameCS.ast and
[A] IteratorExpCS.ast.body = OclExpressionCS[2].ast
-- Alternative B is an implicit collect of an operation over a collection
[B] IteratorExpCS.ast.iterator.type =
OclExpressionCS.ast.type.oclAsType (CollectionType).elementType
[B] IteratorExpCS.ast.source = OclExpressionCS.ast
[B] IteratorExpCS.ast.name = ’collect’
[B] -- the body of the implicit collect is the operation call referred to by ’name’
IteratorExpCS.ast.body.oclIsKindOf (OperationCallExp) and
let body : OperationCallExp = IteratorExpCS.ast.body.oclAsType(OperationCallExp)
in
body.arguments = argumentsCS.ast
and
body.source.oclIsKindOf(VariableExp)
and
body.source.oclAsType (VariableExp).referredVariable = IteratorExpCS.ast.iterator
and
body.referredOperation =
OclExpressionCS.ast.type.oclAsType (CollectionType ).elementType
73
.lookupOperation( simpleNameCS.ast,
if (argumentsCS->notEmpty())
then arguments.ast->collect(type)
else Sequence{} endif)
-- Alternative C/D is an implicit collect of an association or attribute over a collection
[C, D] IteratorExpCS.ast.iterator.type =
OclExpressionCS.ast.type.oclAsType (CollectionType).elementType
[C, D] IteratorExpCS.ast.source = OclExpressionCS.ast
[C, D] IteratorExpCS.ast.name = ’collect’
[C] -- the body of the implicit collect is the attribute referred to by ’name’
let refAtt : Attribute = OclExpressionCS.ast.type.oclAsType (CollectionType).
elementType.lookupAttribute( simpleNameCS.ast),
in
IteratorExpCS.ast.body.oclIsKindOf (AttributeCallExp) and
let body : AttributeCallExp = IteratorExpCS.ast.body.oclAsType(AttributeCallExp)
in
and
and
body.referredAttribute = refAtt
[D] -- the body of the implicit collect is the navigation call referred to by ’name’
let refNav : AssociationEnd = OclExpressionCS.ast.type.oclAsType (CollectionType).
elementType.lookupAssociationEnd(simpleNameCS.ast)
in
IteratorExpCS.ast.body.oclIsKindOf (AssociationEndCallExp) and
let body : AssociationEndCallExp =
IteratorExpCS.ast.body.oclAsType(AssociationEndCallExp)
in
and
and
body.referredAssociationEnd = refNav
and
body.ast.qualifiers = argumentsCS.ast
[E] -- the body of the implicit collect is the navigation to the association class
-- referred to by ’name’
let refClass : AssociationClass =
OclExpressionCS.ast.type.oclAsType (CollectionType).
elementType.lookupAssociationClass(simpleNameCS.ast)
in
IteratorExpCS.ast.body.oclIsKindOf (AssociationClassCallExp) and
let body : AssociationClassCallExp =
IteratorExpCS.ast.body.oclAsType(AssociationClassCallExp)
in
and
and
body.referredAssociationClass = refNav
and
body.ast.qualifiers = argumentsCS.ast
74
[A] OclExpressionCS[1].env = IteratorExpCS.env
[A] VariableDeclarationCS.env = IteratorExpCS.env
-- inside an iterator expression the body is evaluated with a new environment that
-- includes the iterator variable.
[A] OclExpressionCS[2].env =
IteratorExpCS.env.nestedEnvironment().addElement(VariableDeclarationCS.ast.varName,
VariableDeclarationCS.ast,
true)
[B] OclExpressionCS.env = IteratorExpCS.env
[B] argumentsCS.env
= IteratorExpCS.env
[C] OclExpressionCS.env = IteratorExpCS.env
[D] OclExpressionCS.env = IteratorExpCS.env
[1] [A] When the variable declaration is present, it may not have an init expression.
VariableDeclarationCS->notEmpty() implies
VariableDeclarationCS.ast.initExpression->isEmpty()
[2] [B] The source must be of a collection type.
OclExpressionCS.ast.type.oclIsKindOf(CollectionType)
[3] [C] The source must be of a collection type.
OclExpressionCS.ast.type.oclIsKindOf(CollectionType)
[4] [C] The referred attribute must be present.
refAtt->notEmpty()
[5] [D] The referred navifation must be present.
refNav->notEmpty()
IterateExpCS
IterateExpCS ::= OclExpressionCS[1] ’->’ ’iterate’
’(’ (VariableDeclarationCS[1] ’;’)?
VariableDeclarationCS[2] ’|’
OclExpressionCS[2]
’)’
IterateExpCS.ast : IterateExp
-- the ast needs to be determined bit by bit, first the source association of IterateExp
IterateExpCS.ast.source = OclExpressionCS[1].ast
-- next the iterator association of IterateExp
-- when the first variable declaration is present, its ast is the iterator of this
-- iterateExp, when the variable declaration is not present, the iterator has a default
-- name and type,
-- in any case, the iterator has an empty init expression.
IterateExpCS.ast.iterator.name = if VariableDeclarationCS[1]->isEmpty() then ’’
else VariableDeclarationCS[1].ast.name
endif
IterateExpCS.ast.iterator.type =
75
then
else
endif
IterateExpCS.ast.iterator.initExpression->isEmpty()
-- next the name attribute and body and result association of the IterateExp
IterateExpCS.ast.result = VariableDeclarationCS[2].ast
IterateExpCS.ast.name = ’iterate’
IterateExpCS.ast.body = OclExpressionCS[2].ast
OclExpressionCS[1].env
= IteratorExpCS.env
VariableDeclarationCS[1].env = IteratorExpCS.env
VariableDeclarationCS[2].env = IteratorExpCS.env
-- Inside an iterate expression the body is evaluated with a new environment that includes
-- the iterator variable and the result variable.
OclExpressionCS[2].env
=
IteratorExpCS.env.nestedEnvironment().addElement
(VariableDeclarationCS[1].ast.varName,
VariableDeclarationCS[1].ast,
true).addElement
(VariableDeclarationCS[2].ast.varName,
VariableDeclarationCS[2].ast,
true)
[1] A result variable declaration must have a type and an initial value
not VariableDeclarationCS[2].ast.type.oclIsUndefined() VariableDeclarationCS[2].ast.initExpression->notEmpty()
[2] When the first variable declaration is present, it may not have an init expression.
VariableDeclarationCS[1]->notEmpty() implies
VariableDeclarationCS[1].ast.initExpression->isEmpty()
VariableDeclarationCS
In the variable declaration, the type and init expression are optional. When these are required, this is defined in the
production rule where the variable declaration is used.
VariableDeclarationCS ::= simpleNameCS (’:’ typeCS)?
( ’=’ OclExpressionCS )?
VariableDeclarationCS.ast : VariableDeclaration
Synthesised attributes
VariableDeclarationCS.ast.name
= simpleNameCS.ast
VariableDeclarationCS.ast.initExpression = OclExpressionCS.ast
-- A well-formed VariableDeclaration must have a type according to the abstract syntax.
-- The value OclUndefined is used when no type has been given in the concrete syntax.
-- Production rules that use this need to check on this type.
76
VariableDeclarationCS.ast.type = if typeCS->notEmpty() then
typeCS.ast
else
OclUndefined
endif
OclExpressionCS.env = VariableDeclarationCS.env
typeCS.env
= VariableDeclarationCS.env
-- none
TypeCS
A typename is either a Classifier, or a collection of some type.
[A] typeCS ::= pathNameCS
[B] typeCS ::= collectionTypeCS
[C] typeCS ::= tupleTypeCS
typeCS.ast : Classifier
[A] typeCS.ast =
typeCS.env.lookupPathName(pathNameCS.ast).referredElement.oclAsType(Classifier)
[B] typeCS.ast = CollectionTypeCS.ast
[C] typeCS.ast = tupleTypeCS.ast
[B] collectionTypeCS.env = typeCS.env
[C] tupleTypeCS.env = typeCS.env
[1] [A] pathName must be a name of a Classifier in current environment.
typeCS.env.lookupPathName(pathNameCS.ast).referredElement.oclIsKindOf (Classifier)
collectionTypeCS
A typename is either a Classifier, or a collection of some type.
collectionTypeCS ::= collectionTypeIdentifierCS ’(’ typeCS ’)’
typeCS.ast : CollectionType
collectionTypeCS.ast.elementType = typeCS.ast
-- We know that the ’ast’ is a collectiontype, all we need to state now is which
-- specific collection type it is.
77
kind = CollectionKind::Set
implies collectionTypeCS.ast.oclIsKindOf (SetType )
kind = CollectionKind::Sequence implies collectionTypeCS.ast.oclIsKindOf (SequenceType)
kind = CollectionKind::Bag
implies collectionTypeCS.ast.oclIsKindOf (BagType )
kind = CollectionKind::Collection implies collectionTypeCS.ast.oclIsKindOf
(CollectionType)
kind = CollectionKind::OrderedSet
implies collectionTypeCS.ast.oclIsKindOf
(OrderedSetType)
typeCS.env = collectionTypeCS.env
-- none
tupleTypeCS
This represents a tuple type declaration.
tupleTypeCS ::= ’Tuple’ ’(’ variableDeclarationListCS? ’)’
typeCS.ast : TupleType
typeCS.ast = TupleType::make( variableDeclarationListCS->collect( v | v.asAttribute() ))
variableDeclarationListCS.env = tupleTypeCS.env
[1] Of all VariableDeclarations the initExpression must be empty and the type must exist.
variableDeclarationListCS.ast->forAll( varDecl |
varDecl.initExpression->notEmpty() and varDecl.type->notEmpty() )
variableDeclarationListCS
This production rule represents the formal parameters of a tuple or attribute definition.
variableDeclarationListCS[1] = VariableDeclarationCS
(’,’variableDeclarationListCS[2] )?
variableDeclarationListCS[1].ast : Sequence( VariableDeclaration )
variableDeclarationListCS[1].ast = Sequence{VariableDeclarationCS.ast}
->union(variableDeclarationListCS[2].ast)
VariableDeclarationCS.env
= variableDeclarationListCS[1].env
variableDeclarationListCS[2].env = variableDeclarationListCS[1].env
78
-- none
ModelPropertyCallExpCS
A ModelPropertCall expression may have three different productions. Which one is chosen depends on the
disambiguating rules defined in each of the alternatives.
[A] ModelPropertyCallExpCS ::= OperationCallExpCS
[B] ModelPropertyCallExpCS ::= AttributeCallExpCS
[C] ModelPropertyCallExpCS ::= NavigationCallExpCS
ModelPropertyCallExpCS.ast : ModelPropertyCallExp
The value of this production is the value of its child production.
[A] ModelPropertyCallExpCS.ast = OperationCallExpCS.ast
[B] ModelPropertyCallExpCS.ast = AttributeCallExpCS.ast
[C] ModelPropertyCallExpCS.ast = NavigationCallExpCS.ast
[A] OperationCallExpCS.env = ModelPropertyCallExpCS.env
[B] AttributeCallExpCS.env = ModelPropertyCallExpCS.env
[C] NavigationCallExpCS.env = ModelPropertyCallExpCS.env
These are defined in the children.
OperationCallExpCS
An operation call has many different forms. A is used for infix, B for using an object as an implicit collection. C is a
straightforward operation call, while D has an implicit source expression. E and F are like C and D, with the @pre
addition. G covers the class operation call. Rule H is for unary prefix expressions.
[A] OperationCallExpCS ::= OclExpressionCS[1]
simpleNameCS OclExpressionCS[2]
[B] OperationCallExpCS ::= OclExpressionCS ’->’ simpleNameCS ’(’
argumentsCS? ’)’
[C] OperationCallExpCS ::= OclExpressionCS ’.’ simpleNameCS
’(’ argumentsCS? ’)’
[D] OperationCallExpCS ::= simpleNameCS ’(’ argumentsCS? ’)’
[E] OperationCallExpCS ::= OclExpressionCS ’.’ simpleNameCS
isMarkedPreCS ’(’ argumentsCS? ’)’
[F] OperationCallExpCS ::= simpleNameCS isMarkedPreCS ’(’ argumentsCS? ’)’
[G] OperationCallExpCS ::= pathNameCS ’(’ argumentsCS? ’)’
[H] OperationCallExpCS ::= simpleNameCS OclExpressionCS
79
OperationCallExpCS.ast : OperationCallExp
-- this rule is for binary operators as ’+’, ’-’, ’*’ etc. It has only one argument.
[A] OperationCallExpCS.ast.arguments = Sequence{OclExpression2[2].ast}
OperationCallExpCS.ast.source = OclExpressionCS[1].ast
OperationCallExpCS.ast.referredOperation =
OclExpressionCS.ast.type.lookupOperation (
simpleNameCS.ast,
Sequence{OclExpression[2].ast.type} )
-- The source is either a collection or a single object used as a collection.
[B] OperationCallExpCS.ast.arguments = argumentsCS.ast
-- if the OclExpressionCS is a collectiontype, then the source is this OclExpressionCS.
-- Otherwise, the source must be build up by defining a singleton set containing
-- the OclExpressionCS. This is done though inserting a call to the standard
-- operation "asSet()"
OperationCallExpCS.ast.source =
if OclExpressionCS.ast.type.oclIsKindOf(CollectionType)
then OclExpressionCS.ast
else OclExpressionCS.ast.withAsSet()
endif
---- The referred operation:
if OclExpressionCS.ast.type.oclIsKindOf (CollectionType)
then -- this is a collection operation called on a collection
OclExpressionCS.ast.type.lookupOperation (simpleNameCS.ast,
then argumentsCS.ast->collect(type)
else Sequence{} endif )
else
-- this is a set operation called on an object => implicit Set with one element
SetType.allInstances()->any (st |
st.elementType = OclExpressionCS.ast.type).lookupOperation (
simpleNameCS.ast,
then argumentsCS.ast->collect(type)
else Sequence{} endif )
endif
[C] OperationCallExpCS.ast.referredOperation =
if argumentsCS->notEmpty()
OperationCallExpCS.ast.arguments = argumentsCS.ast
OperationCallExpCS.ast.source = OclExpressionCS.ast
[D] OperationCallExpCS.ast.arguments
= argumentsCS.ast and
env.lookupImplicitOperation(simpleName.ast,
OperationCallExpCS.ast.source = env.lookupImplicitSourceForOperation(
80
simpleName.ast,
[E] -- incorporate the isPre() operation.
OperationCallExpCS.ast.arguments = argumentsCS.ast
OperationCallExpCS.ast.source = OclExpressionCS.ast.withAtPre()
[F] -- incorporate atPre() operation with the implicit source
OperationCallExpCS.ast.arguments
env.lookupImplicitOperation(simpleName.ast,
)
OperationCallExpCS.ast.source =
env.lookupImplicitSourceForOperation(simpleName.ast,
).withAtPre()
[G] OperationCallExpCS.ast.arguments
env.lookupPathName(pathName.ast,
OperationCallExpCS.ast.source->isEmpty()
-- this rule is for unary operators as ’-’ and ’not’ etc. It has no argument.
[H] OperationCallExpCS.ast.arguments->isEmpty()
OperationCallExpCS.ast.source = OclExpressionCS.ast
OclExpressionCS.ast.type.lookupOperation (
simpleNameCS.ast,
Sequence{} )
[A] OclExpressionCS[1].env = OperationCallExpCS.env
[A] OclExpressionCS[2].env = OperationCallExpCS.env
[B] OclExpressionCS.env = OperationCallExpCS.env
[B] argumentsCS.env
= OperationCallExpCS.env
[C] OclExpressionCS.env = OperationCallExpCS.env
[C] argumentsCS.env
[D] argumentsCS.env
[E] OclExpressionCS.env = OperationCallExpCS.env
[E] argumentsCS.env
[F] argumentsCS.env
81
[1] [A] The name of the referred Operation must be an operator
Set{’+’,’-’,’*’,’/’,’and’,’or’,’xor’,’=’,’<=’,’>=’,’<’,’>’}->includes(simpleNameCS.ast)
[2] [A,B,C,D,E,F] The referred Operation must be defined for the type of source
not OperationCallExpCS.ast.referredOperation.oclIsUndefined()
[3] [C] The name of the referred Operation cannot be an operator.
Set{’+’,’-’,’*’,’/’,’and’,’or’,’xor’,’=’,’<=’,’>=’,’<’,’>’}->excludes(simpleNameCS.ast)
AttributeCallExpCS
This production rule results in an AttributeCallExp. In production [A] the source is explicit, while production [B] is used
for an implicit source. Alternative C covers the use of a classifier scoped attribute.
[A] AttributeCallExpCS ::= OclExpressionCS ’.’ simpleNameCS isMarkedPreCS?
[B] AttributeCallExpCS ::= simpleNameCS isMarkedPreCS?
[C] AttributeCallExpCS ::= pathNameCS
AttributeCallExpCS.ast : AttributeCallExp
[A] AttributeCallExpCS.ast.referredAttribute =
OclExpressionCS.ast.type.lookupAttribute(simpleNameCS.ast)
[A] AttributeCallExpCS.ast.source = if isMarkedPreCS->isEmpty()
else OclExpressionCS.ast.withAtPre()
endif
[B] AttributeCallExpCS.ast.referredAttribute =
env.lookupImplicitAttribute(simpleNameCS.ast)
[B] AttributeCallExpCS.ast.source =
if isMarkedPreCS->isEmpty()
then env.findImplicitSourceForAttribute(simpleNameCS.ast)
else env.findImplicitSourceForAttribute(simpleNameCS.ast).withAtPre()
endif
[C] AttributeCallExpCS.ast.referredAttribute =
env.lookupPathName(pathNameCS.ast).oclAsType(Attribute)
[A] OclExpressionCS.env = AttributeCallExpCS.env
[1] [A, B] ’simpleName’ is name of an Attribute of the type of source or if source is empty the name of an attribute of ’self’ or
any of the iterator variables in (nested) scope. In OCL:
not AttributeCallExpCS.ast.referredAttribute.oclIsUndefined()
[2] [C] The pathName refers to a class attribute.
env.lookupPathName(pathNameCS.ast).oclIsKindOf(Attribute)
and
AttributeCallExpCS.ast.referredAttribute.ownerscope = ScopeKind::instance
82
NavigationCallExpCS
This production rule represents a navigation call expression.
[A] NavigationCallExpCS ::= AssociationEndCallExpCS
[B] NavigationCallExpCS ::= AssociationClassCallExpCS
NavigationCallExpCS.ast : NavigationCallExp
The value of this production is the value of its child production.
[A] NavigationCallExpCS.ast = AssociationEndCallExpCS.ast
[B] NavigationCallExpCS.ast = AssociationClassCallExpCS.ast
[A] AssociationEndCallExpCS.env = NavigationCallExpCS.env
[B] AssociationClassCallExpCS.env = NavigationCallExpCS.env
These are defined in the children.
AssociationEndCallExpCS
This production rule represents a navigation through an association end. Rule A is the default, rule B is used with an
implicit source, while rule C is used with qualifiers.
[A] AssociationEndCallExpCS ::= OclExpressionCS ’.’ simpleNameCS
(’[’ argumentsCS ’]’)? isMarkedPreCS?
[B] AssociationEndCallExpCS ::= simpleNameCS
AssociationEndCallExpCS.ast : AssociationEndCallExp
[A] AssociationEndCallExpCS.ast.referredAssociationEnd =
OclExpressionCS.ast.type.lookupAssociationEnd(simpleNameCS.ast)
AssociationEndCallExpCS.ast.source = if isMarkedPreCS->isEmpty()
endif
[A] AssociationEndCallExpCS.ast.qualifiers = argumentsCS.ast
[B] AssociationEndCallExpCS.ast.referredAssociationEnd =
env.lookupImplicitAssociationEnd(simpleNameCS.ast)
AssociationEndCallExpCS.ast.source =
then env.findImplicitSourceForAssociationEnd(simpleNameCS.ast)
else env.findImplicitSourceForAssociationEnd(simpleNameCS.ast).withAtPre()
endif
[B] AssociationEndCallExpCS.ast.qualifiers = argumentsCS.ast
83
[A] OclExpressionCS.env = AssociationEndCallExpCS.env
[A, B] argumentsCS.env = AssociationEndCallExpCS.env
[1] [A,B] ’simpleName’ is name of an AssociationEnd of the type of source or if source is empty the name of an AssociationEnd of ’self’ or any of the iterator variables in (nested) scope. In OCL:
not AssociationEndCallExpCS.ast.referredAssociationEnd.oclIsUndefined()
AssociationClassCallExpCS
This production rule represents a navigation to an association class.
[A] AssociationClassCallExpCS ::= OclExpressionCS ’.’ simpleNameCS
[B] AssociationClassCallExpCS ::= simpleNameCS
AssociationClassCallExpCS.ast : AssociationClassCallExp
[A] AssociationClassCallExpCS.ast.referredAssociationClass =
OclExpressionCS.ast.type.lookupAssociationClass(simpleNameCS.ast)
AssociationClassCallExpCS.ast.source = if isMarkedPreCS->isEmpty()
endif
[A] AssociationClassCallExpCS.ast.qualifiers = argumentsCS.ast
[B] AssociationClassCallExpCS.ast.referredAssociationClass =
env.lookupImplicitAssociationClass(simpleNameCS.ast)
AssociationClassCallExpCS.ast.source =
then env.findImplicitSourceForAssociationClass(simpleNameCS.ast)
else env.findImplicitSourceForAssociationClass(simpleNameCS.ast).withAtPre()
endif
[B] AssociationClassCallExpCS.ast.qualifiers = argumentsCS.ast
[A] OclExpressionCS.env = AssociationClassCallExpCS.env
[A, B] argumentsCS.env = AssociationClassCallExpCS.env
[1] ’simpleName’ is name of an AssociationClass of the type of source.
not AssociationClassCallExpCS.ast.referredAssociationClass.oclIsUndefined()
isMarkedPreCS
This production rule represents the marking @pre in an ocl expression.
isMarkedPreCS ::= ’@’ ’pre’
84
isMarkedPreCS.ast : Boolean
self.ast = true
-- none
-- none
argumentsCS
This production rule represents a sequence of arguments.
argumentsCS[1] ::= OclExpressionCS ( ’,’ argumentsCS[2] )?
argumentsCS[1].ast : Sequence(OclExpression)
argumentsCS[1].ast = Sequence{OclExpressionCS.ast}->union(argumentsCS[2].ast)
OclExpressionCS.env = argumentsCS[1].env
argumentsCS[2].env = argumentsCS[1].env
-- none
LetExpCS
This production rule represents a let expression. The LetExpSubCS nonterminal has the purpose of allowing directly
nested let expressions with the shorthand syntax, i.e. ending with one ’in’ keyword.
LetExpCS ::= ’let’ VariableDeclarationCS
LetExpSubCS
LetExpCS.ast : LetExp
LetExpCS.ast.variable = VariableDeclarationCS.ast
LetExpCS.ast.in
= LetExpSubCS.ast
LetExpSubCS.env = LetExpCS.env.nestedEnvironment().addElement(
VariableDeclarationCS.ast.varName,
85
false)
[1] The variable name must be unique in the current scope
LetExpCS.env.lookup (VariableDeclarationCS.ast.varName).oclIsUndefined()
[2] A variable declaration inside a let must have a declared type and an initial value.
not VariableDeclarationCS.ast.type.oclIsUndefined() and
VariableDeclarationCS.ast.initExpression->notEmpty()
LetExpSubCS
[A] LetExpSubCS[1] ::= ’,’ VariableDeclarationCS LetExpSubCS[2]
[B] LetExpSubCS ::= ’in’ OclExpressionCS
LetExpSubCS.ast : OclExpression
[A] LetExpSubCS[1].ast.oclAsType(LetExp).variable
= VariableDeclarationCS.ast
[A] LetExpSubCS[1].ast.oclAsType(LetExp).OClExpression = LetExpSubCS[2].ast
[B] LetExpSubCS.ast = OclExpressionCS.ast
[A] VariableDeclarationCS.env = LetExpSubCS[1].env
[A] LetExpSubCS[2].env = LetExpSubCS[1].env.nestedEnvironment().addElement(
VariableDeclarationCS.ast.varName,
false)
[B] OClExpressionCS.env = LetExpSubCS.env
[A] The variable name must be unique in the current scope
LetExpSubCS[1].env.lookup (VariableDeclarationCS.ast.varName).oclIsUndefined()
[A] A variable declaration inside a let must have a declared type and an initial value.
not VariableDeclarationCS.ast.type.oclIsUndefined() and
VariableDeclarationCS.ast.initExpression->notEmpty()
OclMessageExpCS
The message Name must either be the name of a Signal, or the name of an Operation belonging to the target object(s).
[A] OclMessageExpCS ::= OclExpressionCS ’^^’
simpleNameCS ’(’ OclMessageArgumentsCS? ’)’
[B] OclMessageExpCS ::= OclExpressionCS ’^’
simpleNameCS ’(’ OclMessageArgumentsCS? ’)’
[A] OclMessageExpCS.ast : OclMessageExp
[B] OclMessageExpCS.ast : OclMessageExp
86
[A] OclMessageExpCS.ast.target = OclExpressionCS.ast
[A] OclMessageExpCS.ast.arguments = OclMessageArgumentsCS.ast
-- first, find the sequence of types of the operation/signal parameters
[A] let params : Sequence(Classifier) = OclMessageArguments.ast->collect(messArg |
messArg.getType() ),
-- try to find either the called operation or the sent signal
[A] operation : Operation = OclMessageExpCS.ast.target.type.
lookupOperation(simpleNameCS.ast, params),
signal : Signal = OclMessageExpCS.ast.target.type.
lookupSignal(simpleNameCS.ast, params)
in
OclMessageExpCS.ast.calledOperation = if operation->isEmpty()
then OclUndefined
else = operation
endif
OclMessageExpCS.ast.sentSignal = if signal->isEmpty()
then OclUndefined
else signal
endif
[B]
-- OclExpression^simpleNameCS(OclMessageArguments) is identical to
-- OclExpression^^simpleNameCS(OclMessageArguments)->size() = 1
-- actual mapping: straigthforward, TBD...
OclExpressionCS.env
= OclMessageExpCS.env
OclMessageArgumentsCS.env = OclMessageExpCS.env
-- none
OclMessageArgumentsCS
OclMessageArgumentsCS[1] ::= OclMessageArgCS
( ’,’ OclMessageArgumentsCS[2] )?
OclMessageArgumentsCS[1].ast : Sequence(OclMessageArg)
OclMessageArgumentsCS[1].ast =
Sequence{OclMessageArgCS.ast}->union(OclMessageArgumentsCS[2].ast)
OclMessageArgCS.env
= OclMessageArgumentsCS[1].env
OclMessageArgumentsCS[2].env = OclMessageArgumentsCS[1].env
-- none
87
OclMessageArgCS
[A] OclMessageArgCS ::= ’?’ (’:’ typeCS)?
[B] OclMessageArgCS ::= OclExpressionCS
OclMessageArgCS.ast : OclMessageArg
[A] OclMessageArgCS.ast.expression->isEmpty()
[A] OclMessageArgCS.ast.unspecified->notEmpty()
[A] OclMessageArgCS.ast.type = typeCS.ast
[B] OclMessageArgCS.ast.unspecified->isEmpty()
[B] OclMessageArgCS.ast.expression = OclExpressionCS.ast
OclExpressionCS.env = OclMessageArgCS.env
-- none
IfExpCS
IfExpCS ::= ’if’ OclExpression[1]
’then’ OclExpression[2]
’else’ OclExpression[3]
’endif’
IfExpCS.ast : IfExp
IfExpCS.ast.condition = OclExpression[1].ast
IfExpCS.ast.thenExpression = OclExpression[2].ast
IfExpCS.ast.elseExpression = OclExpression[3].ast
OclExpression[1].env = IfExpCS.env
-- none
88
9.3.1
Comments
It is possible to include comments anywhere in a text composed according to the above concrete syntax. There will be no
mapping of any comments to the abstract syntax. Comments are simply skipped when the text is being parsed. There are
two forms of comments, a line comment and a paragraph comment. The line comment starts with the string ‘--’ and ends
with the next newline. The paragraph comment starts with the string ‘/*’, and ends with the string ‘*/’. Paragraph
comments may be nested.
9.3.2
Operator Precedence
In the grammar, the precedence of the operators from highest to lowest is as follows:
• @pre
• dot and arrow operations: ‘.’ and ‘->’
• unary ‘not’ and unary minus ‘-’
• ‘*’ and ‘/’
• ‘+’ and binary ‘-’
• ‘if-then-else-endif’
• ‘<’, ‘>’, ‘<=’, ‘>=’
• ‘=’, ‘<>’
• ‘and’, ‘or’ and ‘xor’
• ‘implies’
Parentheses ‘(’ and ‘)’ can be used to change precedence.
9.4
Environment definition
The Environment type used in the rules for the concrete syntax is defined according to the following invariants and
additional operations. A diagrammatic view can be found in Figure 13 on page 62. Environments can be nested, denoted
by the existence of a parent environment. Each environment keeps a list of named elements, that have a name a reference
to a ModelElement.
9.4.1
Environment
The definition of Environment has the following invariants and specifications of its operations.
[1] The attribute EMPTY_ENV is really just a helper to avoid having to say new Environment (...).
context Environment
inv EMPTY_ENV_Definition: EMPTY_ENV.namedElements->isEmpty()
[2] Find a named element in the current environment, not in its parents, based on a single name.
context Environment::lookupLocal(name : String) : NamedElement
post: result = namedElements->any(v | v.name = name)
[3] Find a named element in the current environment or recursively in its parent environment, based on a single name.
89
context Environment::lookup(name: String) : ModelElement
post: result = if not lookupLocal(name).oclIsUndefined() then
lookupLocal(name).referredElement
else
parent.lookup(name)
endif
[4] Find a named element in the current environment or recursively in its parent environment, based on a path name.
context Environment::lookupPathName(names: Sequence(String)) : ModelElement
post: let firstNamespace : ModelElement = lookupLocal( names->first() ).referredElement
in
if firstNamespace.isOclKind(Namespace)
-- indicates a sub namespace of the namespace in which self is present
then
result = self.nestedEnvironment().addNamespace(
firstNamespace ).lookupPathName( names->tail() )
else
-- search in surrounding namespace
result = parent.lookupPathName( names )
endif
[5] Add a new named element to the environment. Note that this operation is defined as a query operation so that it can be
used in OCL constraints.
context Environment::addElement (name : String,
elem : ModelElement, imp : Boolean) : Environment
pre : -- the name must not clash with names already existing in this environment
self.lookupLocal(name).oclIsUndefined()
post: result.parent = self.parent and
result.namedElements->includesAll (self.namedElements) and
result.namedElements->count (v | v.oclIsNew()) = 1 and
result.namedElements->forAll (v | v.oclIsNew() implies
v.name = name and v.referredElement = elem)
and
v.mayBeImplicit = imp )
[6] Combine two environments resulting in a new environment. Note that this operation is defined as a query operation so
that it can be used in OCL constraints.
context Environment::addEnvironment(env : Environment) : Environment
pre : -- the names must not clash with names already existing in this environment
enf.namedElements->forAll(nm | self.lookupLocal(nm).oclIsUndefined() )
post: result.parent = self.parent and
result.namedElements = self.namedElements->union(env.namedElements)
[7] Add all elements in the namespace to the environment.
context Environment::addNamespace(ns: Namespace) : Environment
post: result.namedElements = ns.getEnvironmentWithoutParents().namedElements->union(
self.namedElements)
post: result.parent = self.parent
[8] This operation results in a new environment which has the current one as its parent.
context Environment::nestedEnvironment() : Environment
post: result.namedElements->isEmpty()
post: result.parent = self
post: result.oclIsNew()
90
[9] Lookup a given attribute name of an implicitly named element in the current environment, including its parents.
context Environment::lookupImplicitAttribute(name: String) : Attribute
pre: -- none
post: result =
lookupImplicitSourceForAttribute(name).referredElement.oclAsType(Attribute)
[10] Lookup the implicit source belonging to a given attribute name in the current environment, including the parents.
context Environment::lookupImplicitSourceForAttribute(name: String) : NamedElement
pre: -- none
post: let foundElement : NamedElement =
namedElements->select(mayBeImplicit)
->any( ne | not ne.getType().lookupAttribute(name).oclIsUndefined() ) in
result = if foundAttribute.oclIsUndefined() then
self.parent.lookupImplicitSource ForAttribute(name)
else
foundElement
end
[11] Lookup up a given association end name of an implicitly named element in the current environment, including its parents.
context Environment::lookupImplicitAssociationEnd(name: String) : AssociationEnd
pre: -- none
post: let foundAssociationEnd : AssociationEnd =
->any( ne | not ne.getType().lookupAssociationEnd(name).oclIsUndefined() ) in
result = if foundAssociationEnd.oclIsUndefined() then
self.parent.lookupImplicitAssociationEnd(name)
else
foundAssociationEnd
end
[12] Lookup up an operation of an implicitly named element with given name and parameter types in the current environment,
including its parents.
context Environment::lookupImplicitOperation(name: String,
params : Sequence(Classifier)) : Operation
pre: -- none
post: let foundOperation : Operation =
->any( ne | not ne.getType().lookupOperation(name, params).oclIsUndefined() ) in
result = if foundOperation.oclIsUndefined() then
self.parent.lookupImplicitOperation(name)
else
foundOperation
end
9.4.2
NamedElement
A named element is a modelelement which is referred to by a name. A modelement itself has a name, but this is not
always the name which is used to refer to it.
The operation getType() returns the type of the referred modelelement.
context NamedElement::getType() : Classifier
pre: -- none
post: referredElement.oclIsKindOf(VariableDeclaration) implies
result = referredElement.oclAsType(VariableDeclaration).type
91
post: referredElement.oclIsKindOf(Classifier) implies
result = referredElement
post: referredElement.oclIsKindOf(State) implies
result = -- TBD: when aligning with UML 2.0 Infrastructure
9.4.3
Namespace
The following additional operation returns the information of the contents of the namespace in the form of an
Environment object, where Environment is the class defined in this chapter. Note that the parent association of
Environment is not filled.
Because the definition of this operation is completely dependent on the UML metamodel, and this model will be
considerably different in the 2.0 version, the definition is left to be done.
context Namespace::getEnvironmentWithoutParents() : Environment
post: self.isTypeOf(Classifier) implies -- TBD when aligning with UML 2.0 Infrastrcuture
-- include all class features and contained classifiers
post: self.isTypeOf(Package) implies -- TBD when aligning with UML 2.0 Infrastrcuture
-- include all classifiers and subpackages
post: self.isTypeOf(StateMachine)implies -- TBD when aligning with UML 2.0 Infrastrcuture
-- include all states
post: self.isTypeOf(Subsystem) implies -- TBD when aligning with UML 2.0 Infrastrcuture
-- include all classifiers and subpackages
The following operation returns an Environment that contains a reference to its parent environment, which is itself created
by this operation by means of a recursive call, and therefore contains a parent environment too.
context Namespace::getEnvironmentWithParents() : Environment
post: result.NamedElements = self.getEnvironmentWithoutParents()
post: if self.namespace->notEmpty() -- this namespace has an owning namespace
then result.parent = self.namespace.getEnvironmentWithParents()
else result.parent = OclUndefined
endif
9.5
Concrete to Abstract Syntax Mapping
The mapping from concrete to abstract syntax is described as part of the grammar. It is described by adding a synthesized
attribute ast to each production which has the corresponding metaclass from the abstract syntax as its type. This allows
the mapping to be fully formalized within the attribute grammar formalism.
9.6
Abstract Syntax to Concrete Syntax Mapping
IIt is often useful to have a defined mapping from the abstract syntax to the concrete syntax. This mapping can be defined
by applying the production rules in Section 9.3 (“Concrete Syntax”) from left to right. As a general guideline nothing will
be implicit (like e.g implicit collect, implicit use of object as set, etc.), and all iterator variables will be filled in
completely. The mapping is not formally defined in this document but should be obvious.
92
10
Semantics Described using UML
This chapter describes the semantics of the OCL using the UML itself to describe the semantic domain and the mapping
between semantic domain and abstract syntax. It explains the semantics of OCL in a manner based on the report
Unification of Static and Dynamic Semantics for UML [Kleppe2001], which in its turn is based on the MML report
[Clark2000]. The main difference between Appendix A (“Semantics”), which describes the semantics in a formal manner,
and this chapter is that this chapter defines a semantics for the ocl message expression.
10.1
Introduction
In Section 8.3 (“The Expressions Package”) an OCL expression is defined as: "an expression that can be evaluated in a
given environment", and in Section 8.2 (“The Types Package”) it is stated that an "evaluation of the expression yields a
value". The ‘meaning’ (semantics) of an OCL expression, therefore, can be defined as the value yielded by its evaluation
in a given environment.
In order to specify the semantics of OCL expressions we need to define two things: (1) the set of possible values that
evaluations of expressions may yield, and (2) evaluations and their environment. The set of possible values is called the
semantic domain. The set of evaluations together with their associations with the concepts from the abstract syntax
represent the mapping from OCL expressions to values from the semantic domain. Together the semantic domain and the
evaluations with their environment will be called domain in this chapter.
The semantic domain is described in the form of a UML package, containing a UML class diagram, classes, associations,
and attributes. The real semantic domain is the (infinite) set of instances that can be created according to this class
diagram. To represent the evaluation of the OCL expressions in the semantic domain a second UML package is used. In
it, a set of so-called evaluation classes is defined (in short eval). Each evaluation class is associated with a value (its result
value), and a name space environment that binds names to values. Note that the UML model comprising both packages,
resides on layer 1 of the OMG 4-layered architecture, while the abstract syntax defined in Chapter 8 (“Abstract Syntax”),
resides on layer 2.
The semantics of an OCL expression is given by association: each value defined in the semantic domain is associated
with a type defined in the abstract syntax, each evaluation is associated with an expression from the abstract syntax. The
value yielded by an OCL expression in a given environment, its ‘meaning’, is the result value of its evaluation within a
certain name space environment. The semantics are also described in the form of a UML package called "AS-DomainMapping". Note that this package links the domain on layer 1 of the OMG 4-layered architecture with the abstract syntax
on layer 2. The AS-Domain-Mapping package itself can not be positioned in one of the layers of the OMG 4-layered
architecture. Note also that this package contains associations only, no new classes are defined.
Figure 14 on page 94 shows how the packages defined in this chapter relate to each other, and to the packages from the
abstract syntax. It shows the following packages:
• The Domain package describes the values and evaluations. It is subdivided into two subpackages:
• The Values package describes the semantic domain. It shows the values OCL expressions may yield as result.
• The Evaluations package describes the evaluations of OCL expressions. It contains the rules that determine the
result value for a given expression.
• The AS-Domain-Mapping package describes the associations of the values and evaluations with elements from the
abstract syntax. It is subdivided into two subpackages:
93
Ocl-AbstractS ynta x
OCL-Doma in
Typ es
(from Ocl-AbstractSyntax)
V alues
(from OCL-Domain)
Evaluations
(fro m OCL -Do ma in)
Expressions
(from Ocl-AbstractSyntax)
OCL-AS-Domain-Mapping
Type-Value
(from OCL-AS-Domain-Mapping)
Expression-Evaluation
(from OCL-AS-Domain-Mapping)
Figure 14 - Overview of packages in the UML-based semantics
• The Type-Value package contains the associations between the instances in the semantics domain and the types in the
abstract syntax.
• The Expression-Evaluation package contains the associations between the evaluation classes and the expressions in the
abstract syntax.
10.2
The Values Package
OCL is an object language. A value can be either an object, which can change its state in time, or a data type, which can
not change its state. The model in Figure 15 on page 95 shows the values that form the semantic domain of an OCL
expression. The basic type is the Value, which includes both objects and data values. There is a special subtype of Value
called UndefinedValue, which is used to represent the undefined value for any Type in the abstract syntax.
94
DomainElement
0..1
+succ
LocalSnapshot
0 ..1
+pred
+bindings
0..n
+history
{ordered}
NameValueBinding
0..n name : String
1
ObjectValue
+va lue
0 ..n
S taticV alu e
Value
1
OclVo idV alue
Figure 15 - The kernel values in the semantic domain
Figure 16 on page 96 shows a number of special data values, the collection and tuple values. To distinguish between
instances of the Set, Bag, and Sequence types defined in the standard library, and the classes in this package that represent
instances in the semantic domain, the names SetTypeValue, BagTypeValue, and SequenceTypeValue are used, instead of
SetValue, BagValue, and SequenceValue.
The value resulting from an ocl message expression is shown in Figure 17 on page 98. It links an ocl message value to the
snapshot of an object.
10.2.1 Definitions of concepts for the Values package.
The section lists the definitions of concepts in the Values package in alphabetical order.
BagTypeValue
A bag type value is a collection value which is a multiset of values, where each value may occur multiple times in the
bag. The values are unordered. In the metamodel, this list of values is shown as an association from CollectionValue (a
generalization of BagTypeValue) to Element.
CollectionValue
A collection value is a list of values. In the metamodel, this list of values is shown as an association from
CollectionValue to Element.
Associations
•
elements
The values of the elements in a collection.
DomainElement
A domain element is an element of the domain of OCL expressions. It is the generic superclass of all classes defined in
this chapter, including Value and OclExpEval. It serves the same purpose as ModelElement in the UML meta model.
95
+value
1
Value
+value
0..n
StaticValue
NameValueBinding
name : String
+elements
Prim itiveValue
TupleValue
CollectionValue
0..n
0..1
0..1
+elements
EnumValue
0..n
SetTypeValue
Element
indexNr : Integer
SequenceTypeValue
0..n
BagTypeValue
Figure 16 - The collection and tuple values in the semantic domain
Element
An element represents a single component of a tuple value, or collection value. An element has an index number, and a
value. The purpose of the index number is to uniquely identify the position of each element within the enclosing value,
when it is used as an element of a SequenceValue.
LocalSnapshot
A local snapshot is a domain element that holds for one point in time the subvalues of an object value. It is always part
of an ordered list of local snapshots of an object value, which is represented in the metamodel by the associations pred,
succ, and history. An object value may also hold a sequence of OclMessageValues, which the object value has sent, and a
sequence of OclMessageValues, which the object value has received. Both sequences can change in time, therefore they
are included in a local snapshot. This is represented by the associations in the metamodel called inputQ, and outputQ.
A local snapshot has two attributes, isPost and isPre, that indicate whether this snapshot is taken at postcondition or
precondition time of an operation execution. Within the history of an object value it is always possible to find the local
snapshot at precondition time that corresponds with a given snapshot at postcondition time. The association pre (shown in
Figure 17 on page 98) is redundant, but added for convenience.
96
Associations
•
bindings
The set of name value bindings that hold the changes in time of the subvalues of the associated object value.
•
outputQ
The sequence of OclMessageValues that the associated ObjectValue at the certain point in
time has sent, and are not yet put through to their targets.
•
inputQ
The sequence of OclMessageValues that the associated ObjectValue at the certain point in
time has received, but not yet dealt with.
•
pred
The predecessor of this local snapshot in the history of an object value.
•
succ
The successor of this local snapshot in the history of an object value.
•
pre
If this snapshot is a snapshot at postcondition time of a certain operation execution, then
pre is the associated snapshot at precondition time of the same operation in the history of
an object value.
NameValueBinding
A name value binding is a domain element that binds a name to a value.
ObjectValue
An object value is a value that has an identity, and a certain structure of subvalues. Its subvalues may change over time,
although the structure remains the same. Its identity may not change over time. In the metamodel, the structure is shown
as a set of NameValueBindings. Because these bindings may change over time, the ObjectValue is associated with a
sequence of LocalSnapshots, that hold a set of NameValueBindings at a certain point in time.
Associations
•
history
The sequence of local snapshots that hold the changes in time of the subvalues of this
object value.
OclMessageValue
An ocl message value is a value that has as target and as source an object value. An ocl message value has a number of
attributes. The name attribute corresponds to the name of the operation called, or signal sent. The isSyncOperation,
isAsyncOperation, and isSignal attributes indicate respectively whether the message corresponds to a synchronous
operation, an asynchrounous operation, or a signal.
Associations
•
arguments
A sequence of name value bindings that hold the arguments of the message from the
source to the target.
•
source
The object value that has sent this signal.
•
target
The object value for which this signal has been intended.
•
returnMessage
The ocl message value that holds the values of the result and out parameters of a synchronous operation call in its arguments. Is only present if this message represents a synchronous operation call.
OclVoidValue
An undefined value is a value that represents void or undefined for any type.
97
PrimitiveValue
A primitive value is a predefined static value, without any relevant substructure (i.e., it has no parts).
SequenceTypeValue
A sequence type value is a collection value which is a list of values where each value may occur multiple times in the
sequence. The values are ordered by their position in the sequence. In the metamodel, this list of values is shown as an
association from CollectionValue (a generalization of SequenceTypeValue) to Element. The position of an element in
the list is represented by the attribute indexNr of Element.
SetTypeValue
A set type value is a collection value which is a set of elements where each distinct element occurs only once in the set.
The elements are not ordered. In the metamodel, this list of values is shown as an association from CollectionValue (a
generalization of SetTypeValue) to Element.
StaticValue
A static value is a value that will not change over time.1
Value
NameValueBinding
0..n
+arguments
{orde re d}
+target
1
ObjectValue
1
+source
OclMessageValue
name : String
isSyncOperation : Boolean
+returnMessage
isAsyncOperation : Boolean
0..1
isSignal : Boolean
+inputQ
0..n
0..n
0..n
+outp utQ
+history
LocalSnapshot
isPost : Boolean
isPre : Boolean
+pre
0..1
Figure 17 - The message values in the semantic domain
1. As StaticValue is the counterpart of the DataType concept in the abstract syntax, the name DataValue would be preferable. Because this
name is used in the UML 1.4 specification to denote a model of a data value, the name StaticValue is used here.
98
TupleValue
A tuple value (also known as record value) combines values of different types into a single aggregate value. The
components of a tuple value are described by tuple parts each having a name and a value. In the metamodel, this is shown
as an association from TupleValue to NameValueBinding.
Associations
•
elements
The names and values of the elements in a tuple value.
Value
A part of the semantic domain.
10.2.2 Well-formedness rules for the Values Package
BagTypeValue
CollectionValue
DomainElement
Element
EnumValue
LocalSnapshot
[1] Only one of the attributes isPost and isPre may be true at the same time.
context LocalSnapshot
inv: isPost implies isPre = false
inv: ispre implies isPost = false
[2] Only if a snapshot is a postcondition snapshot it has an associated precondition snapshot.
inv: isPost implies pre->size() = 1
inv: not isPost implies pre->size() = 0
inv: self.pre->size() = 1 implies self.pre.isPre = true
NameValueBinding
ObjectValue
[1] The history of an object is ordered. The first element does not have a predecessor, the last does not have a successor.
99
context ObjectValue
inv: history->oclIsTypeOf( Sequence(LocalSnapShot) )
inv: history->last().succ->size = 0
inv: history->first().pre->size = 0
OclMessageValue
[1] Only one of the attributes isSyncOperation, isAsyncOperation, and isSignal may be true at the same time.
context OclMessageValue
inv: isSyncOperation implies isAsyncOperation = false and isSignal = false
inv: isAsyncOperation implies isSyncOperation = false and isSignal = false
inv: isSignal implies isSyncOperation = false and isAsyncOperation = false
[2] The return message is only present if, and only if the ocl message value is a synchronous operation call.
context OclMessageValue
inv: isSyncOperation implies returnMessage->size() = 1
inv: not isSyncOperation implies returnMessage->size() = 0
OclVoidValue
PrimitiveValue
SequenceTypeValue
[1] All elements belonging to a sequence value have unique index numbers.
self.element->isUnique(e : Element | e.indexNr)
SetTypeValue
[1] All elements belonging to a set value have unique values.
self.element->isUnique(e : Element | e.value)
StaticValue
TupleValue
[1] All elements belonging to a tuple value have unique names.
self.elements->isUnique(e : Element | e.name)
Value
10.2.3 Additional operations for the Values Package
LocalSnapshot
[1] The operation allPredecessors returns the collection of all snapshots before a snapshot, allSuccessors returns the
collection of all snapshots after a snapshot.
100
def: let allPredecessors() : Sequence(LocalSnapshot) =
if pred->notEmpty then
pred->union(pred.allPredecessors())
else
Sequence {}
endif
def: let allSuccessors() : Sequence(LocalSnapshot) =
if succ->notEmpty then
succ->union(succ.allSuccessors())
else
Sequence {}
endif
ObjectValue
[1] The operation getCurrentValueOf results in the value that is bound to the name parameter in the latest snapshot in the
history of an object value. Note that the value may be the UndefinedValue.
context ObjectValue::getCurrentValueOf(n: String): Value
pre: -- none
post: result = history->last().bindings->any(name = n).value
[2] The operation outgoingMessages results in the sequence of OclMessageValues that have been in the output queue of
the object between the last postcondition snapshot and its associated precondition snapshot.
context OclExpEval::outgoingMessages() : Sequence( OclMessageValue )
pre: -- none
post:
let end: LocalSnapshot =
history->last().allPredecessors()->select( isPost = true )->first() in
let start: LocalSnapshot = end.pre in
let inBetween: Sequence( LocalSnapshot ) =
start.allSuccessors()->excluding( end.allSuccessors())->including( start ) in
result = inBetween.outputQ->iterate (
-- creating a sequence with all elements present once
m : oclMessageValue;
res: Sequence( OclMessageValue ) = Sequence{}
|
if not res->includes( m )
then res->append( m )
else res
endif )
endif
TupleValue
[1] The operation getValueOf results in the value that is bound to the name parameter in the tuple value.
context TupleValue::getValueOf(n: String): Value
pre: -- none
post: result = elements->any(name = n).value
10.2.4 Overview of the Values package
Figure 18 on page 102 shows an overview of the inheritance relationships between the classes in the Values package.
101
DomainElement
NameValueBinding
ObjectValue
V alu e
Loca lS nap shot
StaticValue
OclMessageValue
Co llectio nV alu e
S etTyp eV alue
TupleValue
BagTypeValue
Element
OclVo idV alue
PrimitiveValue
E numV alue
StringValue
SequenceTypeValue
Figure 18 - The inheritance tree of classes in the Values package
10.3
The Evaluations Package
This section defines the evaluations of OCL expressions. The evaluations package is a mirror image of the expressions
package from the abstract syntax. Figure 19 on page 103 shows how the environment of an OCL expression evaluation is
structured. The environment is determined by the placement of the expression within the UML model as discussed in
Chapter 12 (“The Use of Ocl Expressions in UML Models”). The calculation of the environment is done in the
ExpressionInOclEval, which will be left undefined here.
Figure 20 on page 104 shows the core part of the Evaluations package. The basic elements in the package are the classes
OclEvaluation, PropertyCallExpEval and VariableExpEval. An OclEvaluation always has a result value, and a name
space that binds names to values. In Figure 21 on page 106 the various subtypes of model propertycall evaluation are
defined.
Most of the OCL expressions can be simply evaluated, i.e. their value can be determined based on a non-changing set of
name value bindings. Operation call expressions, however, need the execution of the called operation. The semantics of
the execution of an operation will be defined in the UML infrastructure. For our purposes it is enough to assume that an
102
operation execution will add to the environment of an OCL expression the name ‘result’ bound to a certain value. In order
not to become tangled in a mix of terms, the term evaluation is used in the following to denote both the ‘normal’ OCL
evaluations and the executions of operation call expressions.
In sections 10.3.2 (“Model PropertyCall Evaluations”) to 10.3.6 (“Let expressions”) special subclasses of OclExpEval
will be defined.
10.3.1 Definitions of concepts for the Evaluations package
The section lists the definitions of concepts in the Evaluations package in alphabetical order.
EvalEnvironment
A EvalEnvironment is a set of NameValueBindings that form the environment in which an OCL expression is evaluated.
A EvalEnvironment has three operations which are defined in the section (“Additional operations of the Evaluations
package”).
Associations
•
The NameValueBindings that are the elements of this name space.
bindings
IterateExpEval
An IterateExpEval is an expression evaluation which evaluates its body expression for each element of a collection
value, and accumulates a value in a result variable. It evaluates an IterateExp.
IteratorExpEval
An IteratorExp is an expression evaluation which evaluates its body expression for each element of a collection.
DomainElement
+environment
ExpressionInOclE va l
0..1 +context
1
OclExpEval
1
1
+bindings
1
0 ..n
EvalEnvironment
0..1
NameValueBinding
+environment
1
+be foreE nvironment
Figure 19 - The environment for ocl evaluations
103
+bodyEvals 1. .n
{ordered}
+source
1
+initEx p
OclExpEval
Value
+resultValue
(from Values)
0. .n
1
0. .1
0. .1
PropertyCallEx pEval
LiteralExpEval
VariableExpEval
OclMessageExpEval
0..n
+referredVariable
ModelProperty
Cal lExpEval
LoopExpEval
0. .1
1
StringValue
+iterators
0..n
1..n
(f rom V alues)
1
+name
+result
IteratorExpEval
IterateExpEval
Variab leDecl Eval
0. .n
1
0. .1
Figure 20 - Domain model for ocl evaluations
ExpressionInOclEval
An ExpressionInOclEval is an evaluation of the context of an OCL expression. It is the counterpart in the domain of the
ExpressionInOcl metaclass defined in Chapter 12 (“The Use of Ocl Expressions in UML Models”). It is merely included
here to be able to determine the environment of an OCL expression.
LiteralExpEval
A Literal expression evaluation is an evaluation of a Literal expression.
LoopExpEval
A loop expression evaluation is an evaluation of a Loop expression.
Associations
•
bodyEvals
The oclExpEvaluations that represent the evaluation of the body expression for each element in the source collection.
•
iterators
The names of the iterator variables in the loop expression.
104
ModelPropertyCallExpEval
A model property call expression evaluation is an evaluation of a ModelPropertyCallExp. In Figure 21 on page 106 the
various subclasses of ModelPropertyCallExpEval are shown.
Operations
•
atPre
The atPre operation returns true if the property call is marked as being evaluated at precondition time.
OclExpEval
An ocl expression evaluation is an evaluation of an OclExpression. It has a result value, and it is associated with a set of
name-value bindings, called environment. These bindings represent the values that are visible for this evaluation, and the
names by which they can be referenced. A second set of name-value bindings is used to evaluate any sub expression for
which the operation atPre returns true, called beforeEnvironment.
Note that as explained in chapters 9 (“Concrete Syntax”) and 12 (“The Use of Ocl Expressions in UML Models”), these
bindings need to be established, based on the placement of the OCL expression within the UML model. A binding for an
invariant will not need the beforeEnvironment, and it will be different from a binding of the same expression when used
as precondition.
Associations
•
environment
The set of name value bindings that is the context for this evaluation of an ocl expression.
•
beforeEnvironment
The set of name value bindings at the precondition time of an operation, to evaluate any
sub expressions of type ModelPropertyCallExp for which the operation atPre returns true.
•
resultValue
The value that is the result of evaluating the OclExpression.
OclMessageExpEval
An ocl message expression evaluation is defined in Section 10.3.4 (“Ocl Message Expression Evaluations”), but included
in this diagram for completeness.
PropertyCallExpEval
A property call expression evaluation is an evaluation of a PropertyCallExp.
Associations
•
source
The result value of the source expression evaluation is the instance that performs the property call.
VariableDeclEval
A variable declaration evaluation represents the evaluation of a variable declaration. Note that this is not a subtype of
OclExpEval, therefore it has no resultValue.
Associations
•
name
The name of the variable.
•
initExp
The value that will be initially bound to the name of this evaluation.
105
VariableExpEval
A variable expression evaluation is an evaluation of a VariableExp, which in effect is the search of the value that is bound
to the variable name within the environment of the expression.
Associations
•
variable
The name that refers to the value that is the result of this evaluation.
10.3.2 Model PropertyCall Evaluations
The subtypes of ModelPropertyCallExpEval are shown in Figure 21, and are defined in this section in alphabetical
order.
AttributeCallExpEval
0..n
NavigationCallExpEval 0 ..n
AssociationClassCallExpEval
+navigationSource
0..n
A ssociationEndCallExpEval
{ordered}
+qualifiers 0..n
1
+referredA ssocia tionClass
1
0..n
+referredAssociationEnd 1
+referredAttribute
1
S tring Va lue
(from Values)
+referredOperation
1
OclExpE va l
+argum ents 0..n
1
OperationCallExpEval
0..n
Figure 21 - Domain model for ModelPropertyCallExpEval and subtypes
106
An association end call expression evaluation is an evaluation of a AssociationClassCallExp, which in effect is the search
of the value that is bound to the associationClass name within the expression environment.
Associations
•
referredAssociationClass
The name of the AssociationClass to which the corresponding AssociationClassCallExp
is a reference.
AssociationEndCallExpEval
An association end call expression evaluation is an evaluation of a AssociationEndCallExp, which in effect is the search
of the value that is bound to the associationEnd name within the expression environment.
Associations
•
referredAssociationEnd
The name of the AssociationEnd to which the corresponding NavigationCallExp is a
reference.
An attribute call expression evaluation is an evaluation of an AttributeCallExp, which in effect is the search of the value
that is bound to the attribute name within the expression environment.
Associations
•
referredAttribute
The name of the Attribute to which the corresponding AttributeCallExp is a reference.
NavigationCallExpEval
A navigation call expression evaluation is an evaluation of a NavigationCallExp.
Associations
•
navigationSource
The name of the AssociationEnd of which the corresponding NavigationCallExp is the
source.
OperationCallExp
An operation call expression evaluation is an evaluation of an OperationCallExp.
Associations
•
arguments
The arguments denote the arguments to the operation call. This is only useful when the
operation call is related to an Operation that takes parameters.
•
referredOperation
The name of the Operation to which this OperationCallExp is a reference. This is an
Operation of a Classifier that is defined in the UML model.
10.3.3 If Expression Evaluations
If expression evaluations are shown in Figure 22, and defined in this section.
107
+thenExpression OclExpEval +elseExpression
1
1
+cond ition
1
IfExpEval
Figure 22 - Domain model for if expression
IfExpEval
An IfExpEval is an evaluation of an IfExp.
Associations
•
condition
The OclExpEval that evaluates the condition of the corresponding IfExpression.
•
thenExpression
The OclExpEval that evaluates the thenExpression of the corresponding IfExpression.
•
elseExpression
The OclExpEval that evaluates the elseExpression of the corresponding IfExpression.
10.3.4 Ocl Message Expression Evaluations
Ocl message expressions are used to specify the fact that an object has, or will sent some message to another object at a
some moment in time. Ocl message expresssion evaluations are shown in Figure 23 on page 109, and defined in this
section.
OclMessageArgEval
An ocl message argument evaluation is an evaluation of a OclMessageArg. It represents the evaluation of the actual
parameters to the Operation or Signal. An argument of a message expression is either an ocl expression, or a variable
declaration.
Associations
•
variable
The OclExpEval that represents the evaluation of the argument, in case the argument is a
VariableDeclaration.
•
expression
The OclExpEval that represents the evaluation of the argument, in case the argument is
an OclExpression.
108
Do ma inElem ent
0..1
+expression
Unspe cified Va lue ExpE va l
+unspecified
+target
1
0..1
1
OclExpEval
1
OclMessageArgEval
+arguments
{ordered}
0..n
1
1
OclMe ssag eE xp Eval
name : String
Figure 23 - Domain model for message evaluation
OclMessageExpEval
An ocl message expression evaluation is an evaluation of a OclMessageExp. As explained in [Kleppe2000] the only
demand we can put on the ocl message expression is that the OclMessageValue it represents (either an operation call, or
a UML signal), has been at some time between ‘now’ and a reference point in time in the output queue of the sending
instance. The ‘now’ timepoint is the point in time at which this evaluation is performed. This point is represented by the
environment link of the OclMessageExpEval (inherited from OclExpEval).
Associations
•
target
The OclExpEval that represents the evaluation of the target instance or instances on
which the action is perfomed.
•
arguments
The OclMessageArgEvals that represent the evaluation of the actual parameters to the
Operation or Message.
UnspecifiedValueExpEval
An unspecified value expression evaluation is an evaluation of an UnSpecifiedValueExp. It results in a randomly picked
instance of the type of the expression.
10.3.5 Literal Expression Evaluations
This section defines the different types of literal expression evaluations in OCL, as shown in Figure 24 on page 110.
Again it is a complete mirror image of the abstract syntax.
BooleanLiteralExpEval
A boolean literal expression evaluation represents the evaluation of a boolean literal expression.
109
CollectionItemEval
A collection item evaluation represents the evaluation of a collection item.
CollectionLiteralExpEval
A collection literal expression evaluation represents the evaluation of a collection literal expression.
CollectionLiteralPartEval
A collection literal part evaluation represents the evaluation of a collection literal part.
CollectionRangeEval
A collection range evaluation represents the evaluation of a collection range.
LiteralExpEval
PrimitiveLiteralExpEval
EnumLiteralExpEval
TupleL iteralExpE va l
1
StringLiteralExpEval
+tuplePart 0..n
NumericLiteralExpEval
VariableDeclEval
name : String
0..1
IntegerLiteralExpEval
kind : CollectionKind
1
Value
+pa rts
{ordered}
0..n
+element
1
RealLiteralExpEval
CollectionRangeEval
0 ..1
CollectionItemEval
0..1
0..1
+first 1 +last 1
OclExpEval +item
+initExp
1
1
Figure 24 - Domain model for literal expressions
110
EnumLiteralExpEval
An enumeration literal expression evaluation represents the evaluation of an enumeration literal expression.
A integer literal expression evaluation represents the evaluation of a integer literal expression.
A numeric literal expression evaluation represents the evaluation of a numeric literal expression.
A primitive literal expression evaluation represents the evaluation of a primitive literal expression.
RealLiteralExpEval
A real literal expression evaluation represents the evaluation of a real literal expression.
A string literal expression evaluation represents the evaluation of a string literal expression.
TupleLiteralExpEval
A tuple literal expression evaluation represents the evaluation of a tuple literal expression.
TupleLiteralExpPartEval
A tuple literal expression part evaluation represents the evaluation of a tuple literal expression part.
10.3.6 Let expressions
Let expressions define new variables. The structure of the let expression evaluation is shown in Figure 25.
+in
1
OclExpEval
0..1
0..1
0..1
LetExpEval
0..1
+initExpression
+va ria ble
StringValue
1
Figure 25 - Domain model for let expression
111
LetExpEval
A Let expression evaluation is an evaluation of a Let expression that defines a new variable with an initial value. A Let
expression evaluation changes the environment of the in expression evaluation.
Associations
•
variable
The name of the variable that is defined.
•
in
The expression in whose environment the defined variable is visible.
•
initExpression
The expression that represents the initial value of the defined variable.
10.3.7 Well-formedness Rules of the Evaluations package
The metaclasses defined in the evaluations package have the following well-formednes rules. These rules state how the
result value is determined. This defines the semantics of the OCL expressions.
[1] The result value of an association class call expression is the value bound to the name of the association class to which it
refers. Note that the determination of the result value when qualifiers are present is specified in Section 10.4.3 (“Wellformedness rules for the AS-Domain-Mapping.exp-eval Package”). The operation getCurrentValueOf is an operation
defined on ObjectValue in Section 10.2.3 (“Additional operations for the Values Package”).
context AssociationClassCallExpEval inv:
qualifiers->size = 0 implies
resultValue =
source.resultValue.getCurrentValueOf(referredAssociationClass.name)
[1] The result value of an association end call expression is the value bound to the name of the association end to which it
refers. Note that the determination of the result value when qualifiers are present is specified in Section 10.4.3 (“Wellformedness rules for the AS-Domain-Mapping.exp-eval Package”).
context AssociationEndCallExpEval inv:
qualifiers->size = 0 implies
resultValue =
source.resultValue.getCurrentValueOf(referredAssociationEnd.name)
[1] The result value of an attribute call expression is the value bound to the name of the attribute to which it refers.
context AttributeCallExpEval inv:
resultValue = if source.resultValue->isOclType( ObjectValue) then
source.resultValue->asOclType( ObjectValue )
.getCurrentValueOf(referredAttribute.name)
else -- must be a tuple value
source.resultValue->asOclType( TupleValue )
.getValueOf(referredAttribute.name)
endif
No extra well-formedness rules. The manner in which the resultValue is determined is given in Section 10.4.3 (“Wellformedness rules for the AS-Domain-Mapping.exp-eval Package”).
112
CollectionItemEval
[1] The value of a collection item is the result value of its item expression. The environment of this item expression is equal
to the environment of the collection item evaluation.
context CollectionItemEval
inv: element = item.resultValue
inv: item.environment = self.environment
[1] The environment of its parts is equal to the environment of the collection literal expression evaluation.
context CollectionLiteralExpEval
inv: parts->forAll( p | p.environment = self.environment )
[2] The result value of a collection literal expression evaluation is a collection literal value, or one of its subtypes.
context CollectionLiteralExpEval inv:
resultValue.isOclKind( CollectionValue )
[3] The number of elements in the result value is equal to the number of elements in the collection literal parts, taking into
account that a collection range can result in many elements.
resultValue.elements->size() = parts->collect( element )->size()->sum()
[4] The elements in the result value are the elements in the collection literal parts, taking into account that a collection range
can result in many elements.
let allElements = parts->collect( element )->flatten() in
Sequence{1..allElements->size()}->forAll( i: Integer |
resultValue.elements->at(i).name = ’’ and
resultValue.elements->at(i).value = allElements->at(i) and
self.kind = CollectionKind::Sequence implies
resultValue.elements->at(i).indexNr = i )
No extra well-formedness rules. The manner in which its value is determined is given by its subtypes.
CollectionRangeEval
[1] The value of a collection range is the range of integer numbers between the result value of its first expression and its last
expression.
context CollectionRangeEval
inv: element.isOclType( Sequence(Integer) ) and
element = getRange( first->asOclType(Integer), last->asOclType(Integer) )
EnumLiteralExpEval
No extra well-formedness rules.
EvalEnvironment
[1] All names in a name space must be unique.
context EvalEnvironment inv:
bindings->collect(name)->forAll( name: String | bindings->collect(name)->isUnique(name))
113
ExpressionInOclEval
IfExpEval
[1] The result value of an if expression is the result of the thenExpression if the condition is true, else it is the result of the
elseExpression.
context IfExpEval inv:
resultValue = if condition then thenExpression.resultValue else elseExpression.resultValue
[2] The environment of the condition, thenExpression and elseExpression are both equal to the environment of the if expression.
context IfExpEval
inv: condition.environment = environment
inv: thenExpression.environment = environment
inv: elseExpression.environment = environment
IterateExpEval
[1] All sub evaluations have a different environment. The first sub evaluation will start with an environment in which all iterator variables are bound to the first element of the source, plus the result variable which is bound to the init expression of
the variable declaration in which it is defined.
context IterateExpEval
inv: let bindings: Sequence( NameValueBindings ) =
iterators->collect( i |
NameValueBinding( i.varName, source->asSequence()->first() )
in
bodyEvals->at(1).environment = self.environment->addAll( bindings )
->add( NameValueBinding( result.name, result.initExp.resultValue ))
[2] The environment of any sub evaluation is the same environment as the one from its previous sub evaluation, taking
into account the bindings of the iterator variables, plus the result variable which is bound to the result value of the last
sub evaluation.
inv: let SS: Integer = source.value->size()
in if iterators->size() = 1 then
Sequence{2..SS}->forAll( i: Integer |
bodyEvals->at(i).environment = bodyEvals->at(i-1).environment
->replace( NameValueBinding( iterators->at(1).varName,
source.value->asSequence()->at(i)))
->replace( NameValueBinding( result.varName,
bodyEvals->at(i-1).resultValue )))
else -- iterators->size() = 2
Sequence{2..SS*SS}->forAll( i: Integer |
source->asSequence()->at(i.div(SS) + 1) ))
source.value->asSequence()->at(i.mod(SS))))
->replace( NameValueBinding( result.varName,
114
bodyEvals->at(i-1).resultValue )))
endif
[3] The result value of an IteratorExpEval is the result of the last of its body evaluations.
context IteratorExpEval
inv: resultValue = bodyEvals->last().resultValue
IteratorExpEval
The IteratorExp in the abstract syntax is merely a placeholder for the occurence of one of the predefined iterator
expressions in the standard library (see Chapter 11 (“The OCL Standard Library”)). These predefined iterator expressions
are all defined in terms of an iterate expression. The semantics defined for the iterate expression are sufficient to define
the iterator expression. No well-formedness rules for IteratorExpEval are defined.
LetExpEval
[1] A let expression results in the value of its in expression.
context LetExpEval inv:
resultValue = in.resultValue
[2] A let expression evaluation adds a name value binding that binds the variable to the value of its initExpression, to the
environment of its in expression.
context LetExpEval
inv: in.environment = self.environment
->add( NameValueBinding( variable.varName, variable.initExpression.resultValue ))
[3] The environment of the initExpression is equal to the environment of this Let expression evaluation.
context LetExpEval
inv: initExpression.environment = self.environment
LiteralExpEval
LoopExpEval
The result value of a loop expression evaluation is determined by its subtypes.
[1] There is an OclExpEval (a sub evaluation) for combination of values for the iterator variables. Each iterator variable
will run through every element of the source collection.
context LoopExpEval
inv: bodyEvals->size() =
if iterators->size() = 1 then
source.value->size()
source.value->size() * source.value->size()
endif
[2] All sub evaluations (in the sequence bodyEvals) have a different environment. The first sub evaluation will start with
an environment in which all iterator variables are bound to the first element of the source. Note that this is an
arbitrary choice, one could easily well start with the last element of the source, or any other combination.
context LoopExpEval
inv: let bindings: Sequence( NameValueBindings ) =
iterators->collect( i |
NameValueBinding( i.varName, source->asSequence()->first() )
115
in
bodyEvals->at(1).environment = self.environment->addAll( bindings )
[3] All sub evaluations (in the sequence bodyEvals) have a different environment. The environment is the same
environment as the one from the previous bodyEval, where the iterator variable or variables are bound to the
subsequent elements of the source.
context LoopExpEval
inv:
let SS: Integer = source.value->size()
in if iterators->size() = 1 then
Sequence{2..SS}->forAll( i: Integer |
source.value->asSequence()->at(i) )))
Sequence{2..SS*SS}->forAll( i: Integer |
source->asSequence()->at(i.div(SS) + 1) ))
source.value->asSequence()->at(i.mod(SS)) )) ) ))
endif
Result value is determined by its subtypes.
[1] The environment of an ModelPropertyCall expression is equal to the environment of its source.
context ModelPropertyCallExpEval inv:
environment = source.environment
[1] When the navigation call expression has qualifiers, the result value is limited to those elements for which the
qualifier value equals the value of the attribute.
-- To be done.
No extra well-formedness rules. Result value is determined by its subtypes.
OclExpEval
The result value of an ocl expression is determined by its subtypes.
[1] The environment of an OclExpEval is determined by its context, i.e. the ExpressionInOclEval.
context OclExpEval
inv: environment = context.environment
[2] Every OclExpEval has an environment in which at most one self instance is known.
context OclExpEval
inv: environment->select( name = ’self’ )->size() = 1
OclMessageExpEval
[1] The result value of an ocl message expression is an ocl message value.
116
context OclMessageExpEval
inv: resultValue->isTypeOf( OclMessageValue )
[2] The result value of an ocl message expression is the sequence of the outgoing messages of the ‘self’ object that
matches the expression. Note that this may result in an empty sequence when the expression does not match to any
of the outgoing messages.
inv: resultValue =
environment.getValueOf( ’self’ ).outgoingMessages->select( m |
m.target = target.resultValue and
m.name = self.name and
self.arguments->forAll( expArg: OclMessageArgEval |
not expArg.resultValue.oclIsUndefined() implies
m.arguments->exists( messArg | messArg.value = expArg.value ))
[3] The source of the resulting ocl message value is equal to the ‘self’ object of the ocl message expression.
inv: resultValue.source = environment.getValueOf( ’self’ )
[4] The isSent attribute of the resulting ocl message value is true only if the message value is in the outgoing messages
of the ‘self’ object.
inv:
if resultValue.oclIsUndefined()
resultValue.isSent = false
else
resultValue.isSent = true
endif
[5] The target of an ocl message expression is an object value.
inv: target.resultValue->isTypeOf( ObjectValue )
[6] The environment of all arguments, and the environment of the target expression are equal to the environment of
this ocl message value.
inv: arguments->forAll( a | a.environment = self.environment )
inv: target.environment = self.environment
OclMessageArgEval
[1] An ocl message argument evaluation has either an ocl expression evaluation, or an unspecified value expression
evaluation, not both.
context OclMessageArgEval inv:
expression->size() = 1 implies unspecified->size() = 0
expression->size() = 0 implies unspecified->size() = 1
[2] The result value of an ocl message argument is determined by the result value of its expression, or its unspecified
value expression.
context OclMessageArgEval inv:
if expression->size() = 1
then resultValue = expression.resultValue
else resultValue = unspecified.resultValue
endif
117
[3] The environment of the expression and unspecified value are equal to the environment of this ocl message argument.
context OclMessageArgEval
inv: expression.environment = self.environment
inv: unspecified.environment = self.environment
The definition of the semantics of the operation call expression depends on the definition of operation call execution in
the UML semantics. This is part of the UML infrastructure specification, and will not be defined here. For the semantics
of the OperationCallExp it suffices to know that the execution of an operation call will produce a result of the correct
type. The latter will be specified in Section 10.4 (“The AS-Domain-Mapping Package”).
[1] The environments of the arguments of an operation call expression are equal to the environment of this call.
context OperationCallExpEval inv:
arguments->forall( a | a.environment = self.environment )
PropertyCallExpEval
The result value and environment are determined by its subtypes.
[1] The environment of the source of an property call expression is equal to the environment of this call.
context PropertyCallExpEval inv:
source.environment = self.environment
No extra well-formedness rules. The result value is determined by its subtypes.
RealLiteralExpEval
TupleLiteralExpEval
[1] The result value of a tuple literal expression evaluation is a tuple value whose elements correspond to the parts of the
tuple literal expression evaluation.
context TupleLiteralExpEval inv:
resultValue.isOclType( TupleValue ) and
tuplePart->size() = resultValue.elements->size() and
Sequence{1..tuplePart->size()}->forAll( i: Integer |
resultValue.elements->at(i).name = tuplePart.name and
resultValue.elements->at(i).value = tuplePart.initExpression.resultValue )
The result of an unspecified value expression is a randomly picked instance of the type of the expression. This rule will
be defined in 10.4.3 (“Well-formedness rules for the AS-Domain-Mapping.exp-eval Package”).
118
VariableDeclEval
VariableExpEval
[1] The result of a VariableExpEval is the value bound to the name of the variable to which it refers.
context VariableExpEval inv:
resultValue = environment.getValueOf(referredVariable.varName)
Additional operations of the Evaluations package
EvalEnvironment
[1] The operation getValueOf results in the value that is bound to the name parameter in the bindings of a name space.
Note that the value may be the UndefinedValue.
context EvalEnvironment::getValueOf(n: String): Value
pre: -- none
post: result = bindings->any(name = n).value
[2] The operation replace replaces the value of a name, by the value given in the nvb parameter.
context EvalEnvironment::replace(nvb: NameValueBinding): EvalEnvironment
pre: -- none
post: result.bindings = self.bindings
->excluding( self.bindings->any( name = nvb.name) )->including( nvb )
[3] The operation add adds the name and value indicated by the NameValueBinding given by the nvb parameter.
context EvalEnvironment::add(nvb: NameValueBinding): EvalEnvironment
pre: -- none
post: result.bindings = self.bindings->including( nvb )
[4] The operation addAll adds all NameValueBindings in the nvbs parameter.
context EvalEnvironment::add(nvbs: Collection(NameValueBinding)): EvalEnvironment
pre: -- none
post: result.bindings = self.bindings->union( nvbs )
CollectionRangeEval
[1] The operation getRange() returns a sequence of integers that contains all integer in the collection range.
context CollectionRangeEval::getRange(first, last: Integer): Sequence(Integer)
pre: -- none
post: result = if first = last then
first->asSequence()
else
first->asSequence()->union(getRange(first + 1, last))
endif
10.3.8 Overview of the Values package
Figure 26 on page 120 shows an overview of the inheritance relationships between the classes in the Values package.
119
Dom ai nElem ent
(from Values)
Coll ect ionL ite ra lPartEva l
T upl eLiteralExpPartEval
Expressi onInOcl Eval
OclM essageArgEval
EvalNam eSpace
CollectionItem Eval
Unspe cifi edVal ue ExpEv al
OclExpEval
CollectionRangeEval
PropertyCal lExpEval
Variabl eExpEval
Le tExp Eval
LiteralExpEval
M odelPropertyCal lExpEval
OclM essageExpEval
Lo op ExpEv al
T up l eLi teral ExpEva l
AttributeCall ExpEval
IfExpEval
Enu m Lit eralExp Eva l
Pri m itiveLiteralExpEval
IterateExpEval
IteratorExpEval
Navigati onCall ExpEval
Bool eanLi teral ExpEval
Num ericLi te ral E xpEv al
AssociationClassCall ExpEval
AssociationEndCall ExpEval
Real LiteralExpEval
Figure 26 - The inheritance tree of classes in the Evaluations package
10.4
The AS-Domain-Mapping Package
The figures on page 121 and page 122 show the associations between the abstract syntax concepts and the domain
concepts defined in this chapter. Each domain concept has a counterpart called model in the abstract syntax. Each model
has one or more instances in the semantic domain. Note that in particular every OCL expression can have more than one
evaluation. Still every evaluation has only one value. For example, the "asSequence" applied to a Set may have n!
evaluations, which each give a different permutation of the elements in the set, but each evaluation has exactly one result
value.
120
+instances
0..n
BagTypeValue
+instances
Collectio nV alu e
0 ..n
+instances
EnumValue
+model
+model
CollectionType
(from Types)
1
+model
Enumeration
(from Core)
0..n
+instances
ObjectValue
BagType
(from Types)
1
1
+mo de l
0..n
1
OclMessageValue +instances
+mo de l
Class
(from Core)
OclMessage(T)
(from StandardLibrary)
OclVoidValue
Prim itiveValue
0..n
+instances
0..1
0..n
+instances
StringValue
Value
0 ..n
+instance s
0..n
+instances
0..n
1
+model P rimitive
1 (from Core)
+model S eq uenceType
(from Types)
0..n
+instances
0 ..n
+instances
StaticV alu e
TupleV alue
+instances
VoidType
(from Types)
0..n
+instances
SequenceTypeValue
SetTyp eV alue
1
+model
1
+model
1
+model
+model
1
SetType
(from Types)
DataType
(from Core)
S tring
(from StandardLibrary)
1
+model
TupleType
(from Types)
1
+model
1
Classifier
(from Core)
Figure 27 - Associations between values and the types defined in the abstract syntax.
121
A ssociationC lassC allE xpE val
A ssociationE ndC allE xpE val
+instance s
0..n
+instance s
0..n
A ttributeC allE xpE val +instances
0..n
+instances
B ooleanLiteralE xpE val
0 ..n
+instances
0..n
C ollectionItemE val
C ollectionLiteralE xpE val +instance s
0 ..n
+instances
C ollectionLiteralP artE val
0..n
C ollectionRangeE val + instance s
0..n
+instances
E numLiteralE xpE val
0..n
IfE xpE val
+ mo de l
1
+m odel
A ssociationC lassC allE xp
A ssociationE ndC allE xp
1
+m odel
A ttributeC allE xp
1
+mo de l B ooleanLiteralE xp
1
+m odel
1
+m odel
1
C o llectio nLite ra lE xp
+m odel
1
C ollectionLiteralP art
LetE xpE val
+instances
+m odel
IntegerLiteralE xp
1
+m odel
IterateE xp
0 ..n
+instances
1
+m odel
+instances
0..n
N umericLiteralE xpE val
+ mo de l
1
+m odel
0..n
+instances
0..n
+instances
+ instance s
0..n
1 de l
+mo
NumericLiteralE xp
1
+m odel
+instances
0..n
OclMessageE xpE val
+instances
OperationC allE xpE val
P rimitiveLiteralE xpE val
P ropertyC allE xpE val
+ instance s
0..n
+ instance s
0..n s
+ instance
S tringLiteralE xpE val
OclE xpression
+m odel
OclMessageA rg
OclMe ssag eE xp
1
+m odel
+ mo de l
+m odel
+mo de l1
Op eratio nC allE xp
1 P rim itive Lite ra lE xp
P ropertyC allE xp
RealLiteralE xp
0..n
+ instance s
1
+m odel
S tring Lite ra lE xp
0..n
+instances
1
+m odel
TupleLiteralE xp
1
+m odel
UnspecifiedV alueE xp
T upleLiteralE xpE val
0..n
+instances
Unspecified Va lue ExpE va l
0 ..n
+instances
122
11
1 odel
+m
0..n
+instances
RealLiteralExpE va l
L oo pE xp
NavigationC allE xp
1
+m odel
0 ..n
OclMessageA rgE val
LiteralE xp
1
+mo de l M odelP ropertyC allE xp
OclExpE va l
0..n
LetE xp
1
0..n
+instance s
M od elP ropertyC allE xpE val
N avigationC allE xpE val
Iterato rE xp
+m odel
1
0..n
+instances
V ariableExpE va l
IfE xp
1
0..n
+instances
0..n
LiteralExpE va l +instances
LoopE xpE val
E numLiteralE xp
+ mo de l
1
+ mo de l
Integ erLiteralE xpE val
IteratorE xpE val
C o llectio nRa nge
+m odel
1
+instances
0..n
IterateExpE va l
C ollectionItem
0..n
1
+m odel
V ariableE xp
1
10.4.1 Well-formedness rules for the AS-Domain-Mapping.type-value Package
CollectionValue
[1] All elements in a collection value must have a type that conforms to the elementType of its corresponding CollectionType.
context CollectionValue inv:
elements->forAll( e: Element | e.value.model.conformsTo( model.elementType ) )
DomainElement
Element
EnumValue
ObjectValue
[1] All bindings in an object value must correspond to attributes or associations defined in the object’s Classifier.
context ObjectValue inv:
history->forAll( snapshot | snapshot.bindings->forAll( b |
self.model.allAttributes()->exists (attr | b.name = attr.name)
or
self.model.allAssociationEnds()->exists ( role | b.name = role.name) ) )
OclMessageValue
PrimitiveValue
SequenceTypeValue
SetTypeValue
StaticValue
TupleValue
[1] The elements in a tuple value must have a type that conforms to the type of the corresponding tuple parts.
context TupleValue inv:
elements->forAll( elem |
let correspondingPart: Attribute =
123
self.model.allAttributes()->select( part | part.name = elem.name ) in
elem.value.model.conformsTo( correspondingPart.type ) )
UndefinedValue
Value
10.4.2 Additional operations for the AS-Domain-Mapping.type-value Package
Value
[1] The additional operation isInstanceOf returns true if this value is an instance of the parameter classifier.
context Value::isInstanceOf( c: Classifier ): Boolean
pre: -- none
post: result = self.model.conformsTo( c )
10.4.3 Well-formedness rules for the AS-Domain-Mapping.exp-eval Package
[1] The string that represents the referredAssociationClass in the evaluation must be equal to the name of the referredAssociationClass in the corresponding expression.
context AssociationClassCallExpEval inv:
referredAssociationClass = model.referredAssociationClass.name
[2] The result value of an association class call expression evaluation that has qualifiers, is determined according to the following rule. The ‘normal’ determination of result value is already given in section 10.3.7 (“Well-formedness Rules of the
Evaluations package”).
let
-- the attributes that are the formal qualifiers. Because and association class has two or
-- more association ends, we must select the qualifiers from the other end(s), not from
-- the source of this expression. We allow only 2-ary associations.
formalQualifiers : Sequence(Attribute) =
self.model.referredAssociationClass.connection->any( c |
c <> self.navigationSource).qualifier.asSequence() ,
-- the attributes of the class at the qualified end. Here we already assume that an
-- AssociationEnd will be owned by a Classifier, as will most likely be the case in the
-- UML 2.0 Infrastructure.
objectAttributes: Sequence(Attribute) =
self.model.referredAssociationClass.connection->any( c |
c <> self.navigationSource).owner.feature->select( f |
f.isOclType( Attribute ).asSequence() ,
-- the rolename of the qualified association end
qualifiedEnd: String = self.model.referredAssociationClass.connection->any( c |
c <> self.navigationSource).name ,
-- the values for the qualifiers given in the ocl expression
qualifierValues : Sequence( Value ) = self.qualifiers.asSequence()
124
-- the objects from which a subset must be selected through the qualifiers
normalResult =
source.resultValue.getCurrentValueOf(referredAssociationClass.name)
in
-- if name of attribute of object at qualified end equals name of formal qualifier then
-- if value of attribute of object at qualified end equals the value given in the exp
-- then select this object and put it in the resultValue of this expression.
qualifiers->size <> 0 implies
normalResult->select( obj |
Sequence{1..formalQualifiers->size()}->forAll( i |
objectAttributes->at(i).name = formalQualifiers->at(i).name and
obj.qualifiedEnd.getCurrentValueOf( objectAttributes->at(i).name ) =
qualifiersValues->at(i) ))
[1] The string that represents the referredAssociationEnd in the evaluation must be equal to the name of the referredAssociationEnd in the corresponding expression.
context AssociationEndCallExpEval inv:
referredAssociationEnd = model.referredAssociationEnd.name
[2] The result value of an association end call expression evaluation that has qualifiers, is determined according to the following rule. The ‘normal’ determination of result value is already given in section 10.3.7 (“Well-formedness Rules of the
Evaluations package”).
let
-- the attributes that are the formal qualifiers
formalQualifiers : Sequence(Attribute) = self.model.referredAssociationEnd.qualifier ,
-- the attributes of the class at the qualified end
objectAttributes: Sequence(Attribute) =
(if self.resultValue.model.isOclKind( Collection ) implies
then self.resultValue.model.oclAsType( Collection ).elementType->
collect( feature->asOclType( Attribute ) )
else self.resultValue.model->collect( feature->asOclType( Attribute ) )
endif).asSequence() ,
-- the values for the qualifiers given in the ocl expression
qualifierValues : Sequence( Value ) = self.qualifiers.asSequence()
-- the objects from which a subset must be selected through the qualifiers
normalResult =
source.resultValue.getCurrentValueOf(referredAssociationEnd.name)
in
-- if name of attribute of object at qualified end equals name of formal qualifier then
-- if value of attribute of object at qualified end equals the value given in the exp
-- then select this object and put it in the resultValue of this expression.
qualifiers->size <> 0 implies
normalResult->select( obj |
Sequence{1..formalQualifiers->size()}->forAll( i |
objectAttributes->at(i).name = formalQualifiers->at(i).name and
obj.getCurrentValueOf( objectAttributes->at(i).name ) =
125
qualifiersValues->at(i) ))
[1] The string that represents the referredAttribute in the evaluation must be equal to the name of the referredAttribute in the
corresponding expression.
context AttributeCallExpEval inv:
referredAttribute = model.referredAttribute.name
[1] The result value of a boolean literal expression is equal to the literal expression itself (‘true’ or ‘false’). Because the
booleanSymbol attribute in the abstract syntax is of type Boolean as defined in the MOF, and resultValue is of type Primitive as defined in this chapter, a conversion is neccessary. For the moment, we assume the additional operation MOFbooleanToOCLboolean() exists. This will need to be re-examined when the MOF and/or UML Infrastructure submissions
are finalised.
context BooleanLiteralExpEval inv:
resultValue = model.booleanSymbol.MOFbooleanToOCLboolean()
CollectionItemEval
CollectionRangeEval
EvalEnvironment
Because there is no mapping of name space to an abstract syntax concept, there are no extra well-formedness rules.
LiteralExpEval
LoopExpEval
EnumLiteralExpEval
[1] The result value of an EnumLiteralExpEval must be equal to one of the literals defined in its type.
context EnumLiteralExpEval inv:
model.type->includes( self.resultValue )
126
IfExpEval
[1] The condition evaluation corresponds with the condition of the expression, and likewise for the thenExpression and the
else Expression.
context IfExpEval inv:
condition.model = model.condition
thenExpression.model = model.thenExpression
elseExpression.model = model.elseExpression
context IntegerLiteralExpEval inv:
resultValue = model.integerSymbol
IterateExpEval
[1] The model of the result of an iterate expression evaluation is equal to the model of the result of the associated IterateExp.
context IterateExpEval
inv: result.model = model.result )
IteratorExpEval
LetExpEval
[1] All parts of a let expression evaluation correspond to the parts of its associated LetExp.
context LetExpEval inv:
in.model = model.in and
initExpression.model = model.initExpression and
variable = model.variable.varName
LoopExpEval
[1] All sub evaluations have the same model, which is the body of the associated LoopExp.
context LoopExpEval
inv: bodyEvals->forAll( model = self.model )
[1] The string that represents the navigation source in the evaluation must be equal to the name of the navigationSource in the
corresponding expression.
context NavigationCallExpEval inv:
navigationSource = model.navigationSource.name
[2] The qualifiers of a navigation call expression evaluation must correspond with the qualifiers of the associated expression.
context NavigationCallExpEval inv:
Sequence{1..qualifiers->size()}->forAll( i |
127
qualifiers->at(i).model = model.qualifiers->at(i).type )
OclExpEval
[1] The result value of the evaluation of an ocl expression must be an instance of the type of that expression.
context OclExpEval
inv: resultValue.isInstanceOf( model.type )
OclMessageExpEval
[1] An ocl message expression evaluation must correspond with its message expression.
inv: target.model = model.target
inv: Set{1..arguments->size()}->forall (i | arguments->at(i) = model.arguments->at(i) )
[2] The name of the resulting ocl message value must be equal to the name of the operation or signal indicated in the message
expression.
context OclMessageExpEval inv:
if model.operation->size() = 1
then resultValue.name = model.operation.name
else resultValue.name = model.signal.name
endif
[3] The isSignal, isSyncOperation, and isAsyncOperation attributes of the result value of an ocl message expression evaluation must correspond to the operation indicated in the ocl message expression.
inv:
if model.calledOperation->size() = 1
then model.calledOperation.isAsynchronous = true implies
resultValue.isAsyncOperation = true
else -- message represents sending a signal
resultValue.isSignal = true
endif
[4] The arguments of an ocl message expression evaluation must correspond to the formal input parameters of the operation,
or the attributes of the signal indicated in the ocl message expression.
inv: model.calledOperation->size() = 1 implies
Sequence{1.. arguments->size()} ->forAll( i |
arguments->at(i).variable->size() = 1 implies
model.calledOperation.operation.parameter->
select( kind = ParameterDirectionKind::in )->at(i).name =
arguments->at(i).variable
and
arguments->at(i).expression->size() = 1 implies
model.calledOperation.operation.parameter->
select( kind = ParameterDirectionKind::in )at(i).type =
arguments->at(i).expression.model
inv: model.sentSignal->size() = 1 implies
Sequence{1.. arguments->size()} ->forAll( i |
arguments->at(i).variable->size() = 1 implies
model.sentSignal.signal.feature->select(
arguments->at(i).variable )->notEmpty()
and
arguments->at(i).expression->size() = 1 implies
model.sentSignal.signal.feature.oclAsType(StructuralFeature).type =
128
arguments->at(i).expression.model
[5] The arguments of the return message of an ocl message expression evaluation must correspond to the names given by the
formal output parameters, and the result type of the operation indicated in the ocl message expression. Note that the Parameter type is defined in the UML 1.4 foundation package.
inv: let returnArguments: Sequence{ NameValueBindings ) =
resultValue.returnMessage.arguments ,
formalParameters: Sequence{ Parameter } =
model.calledOperation.operation.parameter
in
resultValue.returnMessage->size() = 1 and model.calledOperation->size() = 1 implies
-- ’result’ must be present and have correct type
returnArguments->any( name = ’result’ ).value.model =
formalParameters->select( kind = ParameterDirectionKind::return ).type
and
-- all ’out’ parameters must be present and have correct type
Sequence{1.. returnArguments->size()} ->forAll( i |
returnArguments->at(i).name =
formalParameters->select( kind = ParameterDirectionKind::out )->at(i).name
and
returnArguments->at(i).value.model =
formalParameters->select( kind = ParameterDirectionKind::out )->at(i).type )
OclMessageArgEval
[1] An ocl message argument evaluation must correspond with its argument expression.
context OclMessageArgEval
inv: model.variable->size() = 1
implies variable->size() = 1 and variable.symbol = model.variable.name
inv: model.expression->size() = 1
implies expression and expression.model = model.expression
[1] The result value of an operation call expression will have the type given by the Operation being called, if the operation has
no out or in/out parmeters, else the type will be a tuple containing all out, in/out parameters and the result value.
context OperationCallEval inv:
let outparameters : Set( Parameter ) = referedOperation.parameter->select( p |
p.kind = ParameterDirectionKind::in/out or
p.kind = ParameterDirectionKind::out)
in
if outparameters->isEmpty()
then resultValue.model = model.referredOperation.parameter
->select( kind = ParameterDirectionKind::result ).type
else resultValue.model.oclIsType( TupleType ) and
outparameters->forAll( p |
resultValue.model.attribute->exist( a | a.name = p.name and a.type = p.type ))
endif
[2] The string that represents the referred operation in the evaluation must be equal to the name of the referredOperation in
the corresponding expression.
referredOperation = model.referredOperation.name
129
[3] The arguments of an operation call expression evaluation must correspond with the arguments of its associated expression.
Sequence{1..arguments->size}->forAll( i |
arguments->at(i).model = model.arguments->at(i) )
PropertyCallExpEval
[1] The source of the evaluation of a property call corresponds to the source of its associated expression.
context PropertyCallExpEval inv:
source.model = model.source
RealLiteralExpEval
context RealLiteralExpEval inv:
resultValue = model.realSymbol
context StringLiteralExpEval inv:
resultValue = model.stringSymbol
TupleLiteralExpEval
context TupleLiteralExpEval inv:
model.tuplePart = tuplePart.model
[1] The result of an unspecified value expression is a randomly picked instance of the type of the expression.
context UnspecifiedValueExpEval
inv: resultValue = model.type.allInstances()->any( true )
inv: resultValue.model = model.type
VariableDeclEval
context VariableDeclEval inv:
model.initExpression = initExpression.model
VariableExpEval
130
11
The OCL Standard Library
This section describes the OCL Standard Library of predefined types, their operations, and predefined expression
templates in the OCL. This section contains all standard types defined within OCL, including all the operations defined
on those types. For each operation the signature and a description of the semantics is given. Within the description, the
reserved word ‘result’ is used to refer to the value that results from evaluating the operation. In several places, post
conditions are used to describe properties of the result. When there is more than one postcondition, all postconditions
must be true. A similar thing is true for multiple preconditions. If these are used, the operation is only defined if all
preconditions evaluate to true.
11.1
Introduction
The structure, syntax and semantics of the OCL is defined in chapters 8 (“Abstract Syntax”), 9 (“Concrete Syntax”) and
10 (“Semantics Described using UML”). This section adds another part to the OCL definition: a library of predefined
types and operations. Any implementation of OCL must include this library package. This approach has also been taken
by e.g. the Java definition, where the language definition and the standard libraries are both mandatory parts of the
complete language definition.
The OCL standard library defines a number of types, which are shown in Figure 28 on page 132. It includes several
primitive types: Integer, Real, String and Boolean. These are familiar from many other languages. The second part of the
standard library consists of the collection types. They are Bag, Set, Sequence and Collection, where Collection is an
abstract type. Note that all types defined in the OCL standard library are instances of an abstract syntax class. The OCL
standard library exists at the modeling level, also referred to as the M1 level, where the abstract syntax is the metalevel
or M2 level.
Next to definitions of types the OCL standard library defines a number of template expressions. Many operations defined
on collections, map not on the abstract syntax metaclass ModelPropertyCallExp, but on the IteratorExp. For each of these
a template expression that defines the name and format of the expression, is defined in Section 11.8 (“Predefined Iterator
Expressions”).
11.2
The OclAny, OclVoid, and OclMessage types
11.2.1 OclAny
The type OclAny is the supertype of all types in the UML model and the primitive types in the OCL Standard Library.
The collection types from the OCL Standard Library are not subtypes of OclAny. Properties of OclAny are available on
each object in all OCL expressions. OclAny is itself an instance of the metatype Classifier.
All classes in a UML model inherit all operations defined on OclAny. To avoid name conflicts between properties in the
model and the properties inherited from OclAny, all names on the properties of OclAny start with ‘ocl.’ Although
theoretically there may still be name conflicts, they can be avoided. One can also use the oclAsType() operation to
explicitly refer to the OclAny properties.
Operations of OclAny, where the instance of OclAny is called object.
131
T
T
O clMessage
O clAny
Collection
T
O clType
O clModelElement
O clS tate
Real
Boolean
S et
T
Bag
T
S equence
S tring
Integer
O clVoid
Figure 28 - The types defined in the OCL standard library
11.2.2 OclMessage
This section contains the definition of the standard type OclMessage. As defined in this section, each ocl message type is
actually a template type with one parameter. ‘T’ denotes the parameter. A concrete ocl message type is created by
substituting an operation or signal for the T.
The predefined type OclMessage is an instance of OclMessageType. Every OclMessage is fully determined by either the
operation, or signal given as parameter. Note that there is conceptually an undefined (infinite) number of these types, as
each is determined by a different operation or signal. These types are unnamed. Every type has as attributes the name of
the operation or signal, and either all formal parameters of the operation, or all attributes of the signal. OclMessage is
itself an instance of the metatype OclMessageType.
OclMessage has a number of predefined operations, as shown in the OCL Standard Library.
132
11.2.3 OclVoid
The type OclVoid is a type that conforms to all other types. It has one single instance called OclUndefined. Any
propertycall applied on OclUndefined results in OclUndefined, except for the operation oclIsUndefined(). OclVoid is
itself an instance of the metatype Classifier.
11.2.4 Operations and well-formedness rules
OclAny
= (object2 : OclAny) : Boolean
True if self is the same object as object2. Infix operator.
post: result = (self = object2)
<> (object2 : OclAny) : Boolean
True if self is a different object from object2. Infix operator.
post: result = not (self = object2)
oclIsNew() : Boolean
Can only be used in a postcondition. Evaluates to true if the self is created during performing the operation. I.e. it didn’t
exist at precondition time.
post: self@pre.oclIsUndefined()
oclIsUndefined() : Boolean
Evaluates to true if the self is equal to OclUndefined.
post: result = self.isTypeOf( OclVoid )
oclAsType(typename : OclType) : T
Evaluates to self, where self is of the type identified by typename. Typename may be in the format
Package::subPackage::classifier.
post: (result = self) and result.oclIsTypeOf( typeName )
oclIsTypeOf(typename : OclType) : Boolean
Evaluates to true if the self is of the type identified by typename. Typename may be in the format
post: -- TBD
oclIsKindOf(typename : OclType) : Boolean
Evaluates to true if the self conforms to the type identified by typename. Typename may be in the format
post: -- TBD
oclIsInState(statename : OclState) : Boolean
Evaluates to true if the self is in the state indentified by statename. Statename may be in the format Class::State::subState.
post: -- TBD
133
allInstances() : Set( T )
Returns all instances of self. Type T is equal to self. May only be used for classifiers that have a finite number of
instances. This is the case for, for instance, user defined classes because instances need to be created explicitly. This is not
the case for, for instance, the standard String, Integer, and Real types.
pre: self.isKindOf( Classifier ) -- self must be a Classifier
and -- TBD
-- self must have a finite number of instances
-- it depends on the UML 2.0 metamodel how this can be
-- expressed
post: -- TBD
11.2.5 OclMessage
hasReturned() : Boolean
True if type of template parameter is an operation call, and the called operation has returned a value. This implies the fact
that the message has been sent. False in all other cases.
post: --
result() : <<The return type of the called operation>>
Returns the result of the called operation, if type of template parameter is an operation call, and the called operation has
returned a value. Otherwise the undefined value is returned.
pre: hasReturned()
isSignalSent() : Boolean
Returns true if the OclMessage represents the sending of a UML Signal.
isOperationCall() : Boolean
Returns true if the OclMessage represents the sending of a UML Operation call.
11.2.6 OclVoid
oclIsUndefined() : Boolean
Evaluates to true if the object is equal to OclUndefined.
post: result = true
[1] OclVoid has only one instance.
context OclVoid inv:
OclVoid.allinstances()->size() = 1
11.3
ModelElement types
This section defines several enumeration types that allow the modeler to refer to elements defined in the UML model.
134
11.3.1 OclModelElement
An OclModelElement is an enumeration. For each element in a UML model there is a corresponding enumeration literal.
OclModelElement is itself an instance of the metatype Enumeration (from UML Core).
11.3.2 OclType
An OclType is an enumeration. For each Classifier in a UML model there is a corresponding enumeration literal.
OclType is itself an instance of the metatype Enumeration (from UML Core).
11.3.3 OclState
An OclState is an enumeration. For each State in a UML model there is a corresponding enumeration literal. OclState is
itself an instance of the metatype Enumeration (from UML Core).
11.3.4 Operations and well-formedness rules
This section contains thye operatiins and well-formedness rules of the model element types.
OclModelElement
= (object : OclType) : Boolean
True if self is the same object as object.
<> (object : OclType) : Boolean
True if self is a different object from object.
post: result = not (self = object)
OclType
= (object : OclType) : Boolean
<> (object : OclType) : Boolean
OclState
= (object : OclState) : Boolean
<> (object : OclState) : Boolean
135
11.4
Primitive Types
The primitive types defined in the OCL standard library are Integer, Real, String and Boolean. They are all instance of the
metaclass Primitive from the UML core package.
11.4.1 Real
The standard type Real represents the mathematical concept of real. Note that Integer is a subclass of Real, so for each
parameter of type Real, you can use an integer as the actual parameter. Real is itself an instance of the metatype Primitive
(from UML Core).
11.4.2 Integer
The standard type Integer represents the mathematical concept of integer. Integer is itself an instance of the metatype
Primitive (from UML Core).
11.4.3 String
The standard type String represents strings, which can be both ASCII or Unicode. String is itself an instance of the
metatype Primitive (from UML Core).
11.4.4 Boolean
The standard type Boolean represents the common true/false values. Boolean is itself an instance of the metatype
Primitive (from UML Core).
11.5
Operations and well-formedness rules
This section contains the operatiins and well-formedness rules of the primitive types.
11.5.1 Real
Note that Integer is a subclass of Real, so for each parameter of type Real, you can use an integer as the actual parameter.
+ (r : Real) : Real
The value of the addition of self and r.
- (r : Real) : Real
The value of the subtraction of r from self.
* (r : Real) : Real
The value of the multiplication of self and r.
- : Real
The negative value of self.
136
/ (r : Real) : Real
The value of self divided by r.
abs() : Real
The absolute value of self.
post: if self < 0 then result = - self else result = self endif
floor() : Integer
The largest integer which is less than or equal to self.
post: (result <= self) and (result + 1 > self)
round() : Integer
The integer which is closest to self. When there are two such integers, the largest one.
post: ((self - result).abs() < 0.5) or ((self - result).abs() = 0.5 and (result > self))
max(r : Real) : Real
The maximum of self and r.
post: if self >= r then result = self else result = r endif
min(r : Real) : Real
The minimum of self and r.
post: if self <= r then result = self else result = r endif
< (r : Real) : Boolean
True if self is less than r.
> (r : Real) : Boolean
True if self is greater than r.
post: result = not (self <= r)
<= (r : Real) : Boolean
True if self is less than or equal to r.
post: result = ((self = r) or (self < r))
>= (r : Real) : Boolean
True if self is greater than or equal to r.
post: result = ((self = r) or (self > r))
11.5.2 Integer
- : Integer
The negative value of self.
137
+ (i : Integer) : Integer
The value of the addition of self and i.
- (i : Integer) : Integer
The value of the subtraction of i from self.
* (i : Integer) : Integer
The value of the multiplication of self and i.
/ (i : Integer) : Real
The value of self divided by i.
abs() : Integer
The absolute value of self.
post: if self < 0 then result = - self else result = self endif
div( i : Integer) : Integer
The number of times that i fits completely within self.
pre : i <> 0
post: if self / i >= 0 then result = (self / i).floor()
else result = -((-self/i).floor())
endif
mod( i : Integer) : Integer
The result is self modulo i.
post: result = self - (self.div(i) * i)
max(i : Integer) : Integer
The maximum of self an i.
post: if self >= i then result = self else result = i endif
min(i : Integer) : Integer
The minimum of self an i.
post: if self <= i then result = self else result = i endif
11.5.3 String
size() : Integer
The number of characters in self.
concat(s : String) : String
The concatenation of self and s.
post: result.size() = self.size() + string.size()
post: result.substring(1, self.size() ) = self
post: result.substring(self.size() + 1, result.size() ) = s
138
substring(lower : Integer, upper : Integer) : String
The sub-string of self starting at character number lower, up to and including character number upper. Character numbers
run from 1 to self.size().
pre: 1 <= lower
pre: lower <= upper
pre: upper <= self.size()
toInteger() : Integer
Converts self to an Integer value.
toReal() : Real
Converts self to a Real value.
11.5.4 Boolean
or (b : Boolean) : Boolean
True if either self or b is true.
xor (b : Boolean) : Boolean
True if either self or b is true, but not both.
post: (self or b) and not (self = b)
and (b : Boolean) : Boolean
True if both b1 and b are true.
not : Boolean
True if self is false.
post: if self then result = false else result = true endif
implies (b : Boolean) : Boolean
True if self is false, or if self is true and b is true.
post: (not self) or (self and b)
11.6
Collection-Related Types
This section defines the collection types and their operations. As defined in this section, each collection type is actually a
template type with one parameter. ‘T’ denotes the parameter. A concrete collection type is created by substituting a type
for the T. So Set (Integer) and Bag (Person) are collection types.
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11.6.1 Collection
Collection is the abstract supertype of all collection types in the OCL Standard Library. Each occurrence of an object in a
collection is called an element. If an object occurs twice in a collection, there are two elements. This section defines the
properties on Collections that have identical semantics for all collection subtypes. Some operations may be defined within
the subtype as well, which means that there is an additional postcondition or a more specialized return value. Collection
is itself an instance of the metatype CollectionType.
The definition of several common operations is different for each subtype. These operations are not mentioned in this
section.
The semantics of the collection operations is given in the form of a postcondtion that uses the IterateExp ot the
IteratorExp construct. The semantics of those constructs is defined in chapter 10 (“Semantics Described using UML”).
In several cases the postcondtion refers to other collection operations, which in turn are defined in terms of the
IterateExp or IteratorExp constructs.
11.6.2 Set
The Set is the mathematical set. It contains elements without duplicates. Set is itself an instance of the metatype SetType.
11.6.3 OrderedSet
The OrderedSet is a Set the elements of which are ordered. It contains no duplicates. OrderedSet is itself an instance of
the metatype OrderedSetType.
11.6.4 Bag
A bag is a collection with duplicates allowed. That is, one object can be an element of a bag many times. There is no
ordering defined on the elements in a bag. Bag is itself an instance of the metatype BagType.
11.6.5 Sequence
A sequence is a collection where the elements are ordered. An element may be part of a sequence more than once.
Sequence is itself an instance of the metatype SequenceType.
11.7
Operations and well-formedness rules
This section contains the operations and well-formedness rules of the collection types.
11.7.1 Collection
size() : Integer
The number of elements in the collection self.
post: result = self->iterate(elem; acc : Integer = 0 | acc + 1)
includes(object : T) : Boolean
True if object is an element of self, false otherwise.
post: result = (self->count(object) > 0)
140
excludes(object : T) : Boolean
True if object is not an element of self, false otherwise.
post: result = (self->count(object) = 0)
count(object : T) : Integer
The number of times that object occurs in the collection self.
post: result = self->iterate( elem; acc : Integer = 0 |
if elem = object then acc + 1 else acc endif)
includesAll(c2 : Collection(T)) : Boolean
Does self contain all the elements of c2 ?
post: result = c2->forAll(elem | self->includes(elem))
excludesAll(c2 : Collection(T)) : Boolean
Does self contain none of the elements of c2 ?
post: result = c2->forAll(elem | self->excludes(elem))
isEmpty() : Boolean
Is self the empty collection?
post: result = ( self->size() = 0 )
notEmpty() : Boolean
Is self not the empty collection?
post: result = ( self->size() <> 0 )
sum() : T
The addition of all elements in self. Elements must be of a type supporting the + operation. The + operation must take one
parameter of type T and be both associative: (a+b)+c = a+(b+c), and commutative: a+b = b+a. Integer and Real fulfill this
condition.
post: result = self->iterate( elem; acc : T = 0 | acc + elem )
product(c2: Collection(T2)) : Set( Tuple( first: T, second: T2) )
The cartesian product operation of self and c2.
post: result = self->iterate (e1; acc: Set(Tuple(first: T, second: T2)) = Set{} |
c2->iterate (e2; acc2: Set(Tuple(first: T, second: T2)) = acc |
acc2->including (Tuple{first = e1, second = e2}) ) )
11.7.2 Set
union(s : Set(T)) : Set(T)
The union of self and s.
post: result->forAll(elem | self->includes(elem) or s->includes(elem))
post: self ->forAll(elem | result->includes(elem))
post: s ->forAll(elem | result->includes(elem))
141
union(bag : Bag(T)) : Bag(T)
The union of self and bag.
post: result->forAll(elem | result->count(elem) = self->count(elem) + bag->count(elem))
post: self->forAll(elem | result->includes(elem))
post: bag ->forAll(elem | result->includes(elem))
= (s : Set(T)) : Boolean
Evaluates to true if self and s contain the same elements.
post: result = (self->forAll(elem | s->includes(elem)) and
s->forAll(elem | self->includes(elem)) )
intersection(s : Set(T)) : Set(T)
The intersection of self and s (i.e, the set of all elements that are in both self and s).
post: result->forAll(elem | self->includes(elem) and s->includes(elem))
post: self->forAll(elem | s ->includes(elem) = result->includes(elem))
post: s ->forAll(elem | self->includes(elem) = result->includes(elem))
intersection(bag : Bag(T)) : Set(T)
The intersection of self and bag.
post: result = self->intersection( bag->asSet )
– (s : Set(T)) : Set(T)
The elements of self, which are not in s.
post: result->forAll(elem | self->includes(elem) and s->excludes(elem))
post: self ->forAll(elem | result->includes(elem) = s->excludes(elem))
including(object : T) : Set(T)
The set containing all elements of self plus object.
post: result->forAll(elem | self->includes(elem) or (elem = object))
post: self- >forAll(elem | result->includes(elem))
post: result->includes(object)
excluding(object : T) : Set(T)
The set containing all elements of self without object.
post: result->forAll(elem | self->includes(elem) and (elem <> object))
post: self- >forAll(elem | result->includes(elem) = (object <> elem))
post: result->excludes(object)
symmetricDifference(s : Set(T)) : Set(T)
The sets containing all the elements that are in self or s, but not in both.
post: result->forAll(elem | self->includes(elem) xor s->includes(elem))
post: self->forAll(elem | result->includes(elem) = s ->excludes(elem))
post: s ->forAll(elem | result->includes(elem) = self->excludes(elem))
The number of occurrences of object in self.
post: result <= 1
142
flatten() : Set(T2)
If the element type is not a collection type this result in the same self. If the element type is a collection type, the result
is the set containing all the elements of all the elements of self.
post: result = if self.type.elementType.oclIsKindOf(CollectionType) then
self->iterate(c; acc : Set() = Set{} |
acc->union(c->asSet() ) )
else
self
endif
asSet() : Set(T)
A Set identical to self. This operation exists for convenience reasons.
post: result = self
asOrderedSet() : OrderedSet(T)
An OrderedSet that contains all the elements from self, in undefined order.
post: result->forAll(elem | self->includes(elem))
asSequence() : Sequence(T)
A Sequence that contains all the elements from self, in undefined order.
post: self->forAll(elem | result->count(elem) = 1)
asBag() : Bag(T)
The Bag that contains all the elements from self.
post: self->forAll(elem | result->count(elem) = 1)
11.7.3 OrderedSet
append (object: T) : OrderedSet(T)
The set of elements, consisting of all elements of self, followed by object.
post: result->size() = self->size() + 1
post: result->at(result->size() ) = object
post: Sequence{1..self->size() }->forAll(index : Integer |
result->at(index) = self ->at(index))
prepend(object : T) : OrderedSet(T)
The sequence consisting of object, followed by all elements in self.
post: result->size = self->size() + 1
post: result->at(1) = object
post: Sequence{1..self->size()}->forAll(index : Integer |
self->at(index) = result->at(index + 1))
insertAt(index : Integer, object : T) : OrderedSet(T)
The set consisting of self with object inserted at position index.
post: result->at(index) = object
143
post: Sequence{1..(index - 1)}->forAll(i : Integer |
self->at(i) = result->at(i))
post: Sequence{(index + 1)..self->size()}->forAll(i : Integer |
self->at(i) = result->at(i + 1))
subOrderedSet(lower : Integer, upper : Integer) : OrderedSet(T)
The sub-set of self starting at number lower, up to and including element number upper.
pre : 1 <= lower
pre : lower <= upper
pre : upper <= self->size()
post: result->size() = upper -lower + 1
post: Sequence{lower..upper}->forAll( index |
result->at(index - lower + 1) =
self->at(index))
at(i : Integer) : T
The i-th element of self.
pre : i >= 1 and i <= self->size()
indexOf(obj : T) : Integer
The index of object obj in the sequence.
pre : self->includes(obj)
post : self->at(i) = obj
first() : T
The first element in self.
post: result = self->at(1)
last() : T
The last element in self.
post: result = self->at(self->size() )
11.7.4 Bag
= (bag : Bag(T)) : Boolean
True if self and bag contain the same elements, the same number of times.
post: result = (self->forAll(elem | self->count(elem) = bag->count(elem)) and
bag->forAll(elem | bag->count(elem) = self->count(elem)) )
union(bag : Bag(T)) : Bag(T)
The union of self and bag.
post: result->forAll( elem | result->count(elem) = self->count(elem) + bag->count(elem))
post: self ->forAll( elem | result->count(elem) = self->count(elem) + bag->count(elem))
post: bag ->forAll( elem | result->count(elem) = self->count(elem) + bag->count(elem))
union(set : Set(T)) : Bag(T)
The union of self and set.
144
post: result->forAll(elem | result->count(elem) = self->count(elem) + set->count(elem))
post: self ->forAll(elem | result->count(elem) = self->count(elem) + set->count(elem))
post: set ->forAll(elem | result->count(elem) = self->count(elem) + set->count(elem))
intersection(bag : Bag(T)) : Bag(T)
The intersection of self and bag.
post: result->forAll(elem |
result->count(elem) = self->count(elem).min(bag->count(elem)) )
post: self->forAll(elem |
post: bag->forAll(elem |
intersection(set : Set(T)) : Set(T)
The intersection of self and set.
post: result->forAll(elem|result->count(elem) = self->count(elem).min(set->count(elem)) )
post: self ->forAll(elem|result->count(elem) = self->count(elem).min(set->count(elem)) )
post: set ->forAll(elem|result->count(elem) = self->count(elem).min(set->count(elem)) )
including(object : T) : Bag(T)
The bag containing all elements of self plus object.
if elem = object then
result->count(elem) = self->count(elem) + 1
else
result->count(elem) = self->count(elem)
endif)
result->count(elem) = self->count(elem) + 1
else
endif)
excluding(object : T) : Bag(T)
The bag containing all elements of self apart from all occurrences of object.
result->count(elem) = 0
else
endif)
result->count(elem) = 0
else
endif)
145
flatten() : Bag(T2)
If the element type is not a collection type this result in the same bag. If the element type is a collection type, the result
is the bag containing all the elements of all the elements of self.
self->iterate(c; acc : Bag() = Bag{} |
acc->union(c->asBag() ) )
else
self
endif
asBag() : Bag(T)
A Bag identical to self. This operation exists for convenience reasons.
post: result = self
A Sequence that contains all the elements from self, in undefined order.
post: result->forAll(elem | self->count(elem) = result->count(elem))
post: self ->forAll(elem | self->count(elem) = result->count(elem))
asSet() : Set(T)
The Set containing all the elements from self, with duplicates removed.
post: result->forAll(elem | self ->includes(elem))
An OrderedSet that contains all the elements from self, in undefined order, with duplicates removed.
post: self ->forAll(elem | result->count(elem) = 1)
11.7.5 Sequence
= (s : Sequence(T)) : Boolean
True if self contains the same elements as s in the same order.
post: result = Sequence{1..self->size()}->forAll(index : Integer |
self->at(index) = s->at(index))
and
self->size() = s->size()
union (s : Sequence(T)) : Sequence(T)
The sequence consisting of all elements in self, followed by all elements in s.
post: result->size() = self->size() + s->size()
self->at(index) = result->at(index))
post: Sequence{1..s->size()}->forAll(index : Integer |
146
s->at(index) = result->at(index + self->size() )))
flatten() : Sequence(T2)
If the element type is not a collection type this result in the same self. If the element type is a collection type, the result
is the seuqnce containing all the elements of all the elements of self. The order of the elements is partial.
self->iterate(c; acc : Sequence() = Sequence{} |
acc->union(c->asSequence() ) )
else
self
endif
append (object: T) : Sequence(T)
The sequence of elements, consisting of all elements of self, followed by object.
post: result->size() = self->size() + 1
post: result->at(result->size() ) = object
post: Sequence{1..self->size() }->forAll(index : Integer |
result->at(index) = self ->at(index))
prepend(object : T) : Sequence(T)
The sequence consisting of object, followed by all elements in self.
post: result->at(1) = object
self->at(index) = result->at(index + 1))
insertAt(index : Integer, object : T) : Sequence(T)
The sequence consisting of self with object inserted at position index.
post: result->at(index) = object
post: Sequence{1..(index - 1)}->forAll(i : Integer |
self->at(i) = result->at(i))
post: Sequence{(index + 1)..self->size()}->forAll(i : Integer |
self->at(i) = result->at(i + 1))
subSequence(lower : Integer, upper : Integer) : Sequence(T)
The sub-sequence of self starting at number lower, up to and including element number upper.
pre : 1 <= lower
pre : lower <= upper
pre : upper <= self->size()
post: result->size() = upper -lower + 1
post: Sequence{lower..upper}->forAll( index |
result->at(index - lower + 1) =
self->at(index))
at(i : Integer) : T
The i-th element of sequence.
pre : i >= 1 and i <= self->size()
147
indexOf(obj : T) : Integer
The index of object obj in the sequence.
pre : self->includes(obj)
post : self->at(i) = obj
first() : T
The first element in self.
post: result = self->at(1)
last() : T
The last element in self.
post: result = self->at(self->size() )
including(object : T) : Sequence(T)
The sequence containing all elements of self plus object added as the last element.
post: result = self.append(object)
excluding(object : T) : Sequence(T)
The sequence containing all elements of self apart from all occurrences of object.
The order of the remaining elements is not changed.
post:result->includes(object) = false
post: result->size() = self->size() - self->count(object)
post: result = self->iterate(elem; acc : Sequence(T)
= Sequence{}|
if elem = object then acc else acc->append(elem) endif )
asBag() : Bag(T)
The Bag containing all the elements from self, including duplicates.
post: result->forAll(elem | self->count(elem) = result->count(elem) )
post: self->forAll(elem | self->count(elem) = result->count(elem) )
The Sequence identical to the object itself. This operation exists for convenience reasons.
post: result = self
asSet() : Set(T)
The Set containing all the elements from self, with duplicated removed.
An OrderedSet that contains all the elements from self, in the same order, with duplicates removed.
post: self ->forAll(elem | result->count(elem) = 1)
post: self ->forAll(elem1, elem2 |
148
self->indexOf(elem1) < self->indexOf(elem2)
implies result->indexOf(elem1) < result->indexOf(elem2) )
11.8
Predefined Iterator Expressions
This section defines the standard OCL iterator expressions. In the abstract syntax these are all instances of IteratorExp.
These iterator expressions always have a collection expression as their source, as is defined in the well-formedness rules
in Chapter 8 (“Abstract Syntax”). The defined iterator expressions are shown per source collection type. The semantics of
each iterator expression is defined through a mapping from the iterator to the ’iterate’ construct. this means that the
semantics of the iterator expressions does not need to be defined seperately in the sementics sections.
Whenever a new itertor is added to the library, the mapping to the iterate expression must be defined. If this is not done,
the semantics of the new iterator is undefined.
In all of the following OCL expressions, the lefthand side of the equals sign is the IteratorExp to be defined, and the
righthand side of the equals sign is the equivalent as an IterateExp. The names source, body and iterator refer to the
role names in the abstract syntax:
•
source
The source expression of the IteratorExp
•
body
The body expression of the IteratorExp
•
iterator
The iterator variable of the IteratorExp
•
result
The result variable of the IterateExp
11.8.1 Extending the standard library with iterator expressions
When new iterator expressions are added to the standard library, there mapping to existing constructs should be fully
defines. If this is done, the semantics of the new iterator expression will be defined.
11.9
Mapping rules for predefined iterator expressions
This section contains the operations and well-formedness rules of the collection types.
11.9.1 Collection
exists
Results in true if body evaluates to true for at least one element in the source collection.
source->exists(iterators | body) =
source->iterate(iterators; result : Boolean = false | result or body)
forAll
Results in true if the body expression evaluates to true for each element in the source collection; otherwise, result is false.
source->forAll(iterators | body ) =
source->iterate(iterators; result : Boolean = true | result and body)
isUnique
Results in true if body evaluates to a different value for each element in the source collection; otherwise, result is false.
source->isUnique (iterators | body) =
149
source->collect (iterators | Tuple{iter = Tuple{iterators}, value = body})
->forAll (x, y | (x.iter <> y.iter) implies (x.value <> y.value))
isUnique may have at most one iterator variable.
any
Returns any element in the source collection for which body evaluates to true. If there is more than one element for which
body is true, one of them is returned. There must be at least one element fulfilling body, otherwise the result of this
IteratorExp is OclUndefined.
source->any(iterator | body) =
source->select(iterator | body)->asSequence()->first()
any may have at most one iterator variable.
one
Results in true if there is exactly one element in the source collection for which body is true.
source->one(iterator | body) =
source->select(iterator | body)->size() = 1
one may have at most one iterator variable.
collect
The Collection of elements which results from applying body to every member of the source set. The result is flattened.
Notice that this is based on collectNested, which can be of different type depending on the type of source. collectNested
is defined individually for each subclass of CollectionType.
source->collect (iterators | body) = source->collectNested (iterators | body)->flatten()
collect may have at most one iterator variable.
11.9.2 Set
The standard iterator expression with source of type Set(T) are:
select
The subset of set for which expr is true.
source->select(iterator | body) =
source->iterate(iterator; result : Set(T) = Set{} |
if body then result->including(iterator)
else result
endif)
select may have at most one iterator variable.
reject
The subset of the source set for which body is false.
source->reject(iterator | body) =
source->select(iterator | not body)
150
reject may have at most one iterator variable.
collectNested
The Bag of elements which results from applying body to every member of the source set.
source->collect(iterators | body) =
source->iterate(iterators; result : Bag(body.type) = Bag{} |
result->including(body ) )
collectNested may have at most one iterator variable.
sortedBy
Results in the OrderedSet containing all elements of the source collection. The element for which body has the lowest
value comes first, and so on. The type of the body expression must have the < operation defined. The < operation must
return a Boolean value and must be transitive i.e. if a < b and b < c then a < c.
source->sortedBy(iterator | body) =
iterate( iterator ; result : OrderedSet(T) : OrderedSet {} |
if result->isEmpty() then
result.append(iterator)
else
let position : Integer = result->indexOf (
result->select (item | body (item) > body (iterator)) ->first() )
in
result.insertAt(position, iterator)
endif
sortedBy may have at most one iterator variable.
11.9.3 Bag
The standard iterator expression with source of type Bag(T) are:
select
The sub-bag of the source bag for which body is true.
source->iterate(iterator; result : Bag(T) = Bag{} |
else result
endif)
reject
The sub-bag of the source bag for which body is false.
151
collectNested
The Bag of elements which results from applying body to every member of the source bag.
source->iterate(iterators; result : Bag(body.type) = Bag{} |
result->including(body ) )
sortedBy
Results in the Sequence containing all elements of the source collection. The element for which body has the lowest value
comes first, and so on. The type of the body expression must have the < operation defined. The < operation must return a
Boolean value and must be transitive i.e. if a < b and b < c then a < c.
iterate( iterator ; result : Sequence(T) : Sequence {} |
else
in
endif
11.9.4 Sequence
The standard iterator expressions with source of type Sequence(T) are:
select(expression : OclExpression) : Sequence(T)
The subsequence of the source sequence for which body is true.
source->iterate(iterator; result : Sequence(T) = Sequence{} |
else result
endif)
reject
The subsequence of the source sequence for which body is false.
collectNested
The Sequence of elements which results from applying body to every member of the source sequence.
152
source->iterate(iterators; result : Sequence(body.type) = Sequence{} |
result->append(body ) )
sortedBy
Results in the Sequence containing all elements of the source collection. The element for which body has the lowest value
comes first, and so on. The type of the body expression must have the < operation defined. The < operation must return a
Boolean value and must be transitive i.e. if a < b and b < c then a < c.
iterate( iterator ; result : Sequence(T) : Sequence {} |
else
in
endif
153
154
12
The Use of Ocl Expressions in UML Models
This section describes the various manners in which OCL expressions can be used in UML models.
12.1
Introduction
In principle, everywhere in the UML specification where the term expression is used, an OCL expression can be used. In
UML 1.4 OCL expressions could be used e.g. for invariants, preconditions and postconditons, but other placements are
possible too. The meaning of the value, which results from the evaluation of the OCL expression, depends on its
placement within the UML model.
In this specification the structure of an expression, and its evaluation are separated from the usage of the expression.
Chapter 8 (“Abstract Syntax”) defines the structure of an expression, and appendix A (“Semantics”) defines the
evaluation. In chapter 9 (“Concrete Syntax”) it was allready noted that the contents of the name space environment of an
OCL expression are fully determined by the placement of the OCL expression in the model. In that chapter an inherited
attribute env was introduced for every production rule in the attribute grammar to represent this name space environment.
This section specifies a number of predefined places where OCL expressions can be used, their associated meaning, and
the contents of the name space environment. The modeler has to define her/his own meaning, if OCL is used at a place in
the UML model which is not defined in this section.
For every occurence of an OCL expression three things need to be separated: the placement, the contextual classifier, and
the self instance of an OCL expression.
• The placement is the position where the OCL expression is used in the UML model, e.g. as invariant connected to class
Person.
• The contextual classifier defines the namespace in which the expression is evaluated. For example, the contextual clas-
sifier of a precondition is the classifier that is the owner of the operation for which the precondition is defined. Visible
within the precondition are all model element that are visible in the contextual classifier.
• The self instance is the reference to the object that evaluates the expression. It is always an instance of the contextual
classifier. Note that evaluation of an OCL expression may result in a different value for every instance of the contextual classifier.
In the next section a number of placements are stated explicitly. For each the contextual classifier is defined, and wellformedness rules are given, that exactly define the place where the OCL expression is attached to the UML model.
12.1.1 UML 2.0 Alignment
The definition of the contextualClassifier and ExpressionInOcl depends to a large extend on the UML 2.0 definition.
Therefore this section will need to be finished after the UML 2.0 definition has been frozen. Therefore not all rules in this
section are completely finished, they need to be re-done anyway.
12.2
The ExpressionInOcl Type
Because in the abstract syntax OclExpression is defined recursively, we need a new metaclass to represent the top of the
abstract syntax tree that represents an OCL expression. This metaclass is called ExpressionInOcl, and it is defined to be a
subclass of the Expression metaclass from the UML core, as shown in Figure 29. In UML (1.4) the Expression metaclass
has an attribute language which may have the value ’OCL’. The body attribute contains a text representation of the actual
155
Expression
(from DataTypes)
+ language
+ body : String
E xp re ssionInOcl
+bodyExpression
OclE xpressio n
1
+contextualClassifier
0 ..1
Classifier
(from Co re)
Figure 29 - Metaclass ExpressionInOcl added to the UML metamodel
expression. The bodyExpression association of ExpressionInOcl is an association to the OCL expression as represented
by the OCL Abstract syntax metamodel. The body attribute (inherited from Expression) may still be used to store the
string representation of the OCL expression. The language attribute (also inherited form Expression) has the value ‘OCL’.
12.2.1 ExpressionInOcl
An expression in OCL is an expression that is written in OCL. The value of the language attribute is therefore always
equal to ‘OCL’.
Associations
•
contextualClassifier
The classifier that is the context of the OCL expression. Self is always an instance of this
classifier. The contextualClassifier is always a derived association. In the remainder of
this chapter many derivations will be given.
•
bodyExpression
The bodyExpression is an OclExpression that is the root of the actual OCL expression,
which is described fully by the OCL abstract syntax metamodel.
12.3
Well-formedness rules
12.3.1 ExpressionInOcl
[1] This expression is always written in OCL
context ExpressionInOcl
inv: language = ’OCL’
156
12.4
Standard placements of OCL Expressions
This section defines the standard places where OCL expressions may occur, and defines for each case the value for the
contextual classifier. Note that this list of places is not exhausting, and can be enhanced.
12.4.1 How to extend the use of OCL at other places
At many places in the UML where an Expression is used, one can write this expression in OCL. To define the use of OCL
at such a place, the main task is to define what the contextual classifier is. When that is given, the OCL expression is fully
defined. This section defines a number of often used placements of OCL expressions.
12.5
Definition
A definition constraint is a constraint that is linked to a Classifier. It may only consist of one or more LetExps. The
variable or function defined by the Let expression can be used in an identical way as an attribute or operation of the
Classifier. Their visibility is equal to that of a public attribute or operation. The purpose of a definition constraint is to
define reusable sub-expressions for use in other OCL expressions.
The placement of a definition constraint in the UML metamodel is shown in Figure 30. The following well-formedness
rule must hold. This rule also defines the value of the contextual Classifier.
12.5.1 Well-formedness rules
[1] The ExpressinInOcl is a definition constraint if it has the stereotype <<definition>> (A) and the constraint is attached to
only one model element (B) and the constraint is attached to a Classifier (C).
def: isDefinitionConstraint : Boolean =
self.constraint.stereotype.name = ’definition’
-- A
and
self.constraint.constrainedElement->size() = 1
-- B
and
self.constraint.constrainedElement.any(true).oclIsKindOf(Classifier) -- C
ModelE lement
(from Core)
+ constraint C o nstra int
0..n
(from Core)
+constrainedE lement 0..n
0 ..1
C lassifier
(from Core)
1 +body
E xpression
(from Da taTyp es )
E xpressionInOcl
+bodyE xpressio n OclE xpression
1
Figure 30 - Situation of Ocl expression used as definition or invariant
157
[2] For a definition constraint the contextual classifier is the constrained element.
inv: isDefinitionConstraint implies
contextualClassifier =
self.constraint.constrainedElement.any(true).oclAsType(Classifier)
[3] Inside a definition constraint the use of @pre is not allowed.
inv: --
12.6
Invariant
An invariant constraint is a constraint that is linked to a Classifier. The purpose of an invariant constraint is to specify
invariants for the Classifier. An invariant constraint consists of an OCL expression of type Boolean. The expression must
be true for each instance of the classifier at any moment in time. Only when an instance is executing an operation, this
does not need to evaluate to true.
The placement of an invariant constraint in the UML metamodel is equal to the placement of a definition constraint,
which is shown in Figure 30. The following well-formedness rule must hold. This rule also defines the value of the
contextual Classifier.
[1] The constraint has the stereotype <<invariant>> (A) and the constraint is attached to only one model element (B) the constraint is attached to a Classifier (C). The contextual classifier is the constrained element and the type of the OCL expression must be Boolean.
inv: self.constraint.stereotype.name = ’invariant’
-- A
and
-- B
and
self.constraint.constrainedElement.any(true).oclIsKindOf(Classifier) -- C
implies
self.constraint.constrainedElement->any(true).oclAsType(Classifier)
and
self.bodyExpression.type.name = ’Boolean’
[2] Inside an invariant constraint the use of @pre is not allowed.
inv: --
12.7
Precondition
A precondition is a constraint that may be linked to an Operation of a Classifier. The purpose of a precondition is to
specify the conditions that must hold before the operation executes. A precondition consists of an OCL expression of type
Boolean. The expression must evaluate to true whenever the operation starts executing, but only for the instance that will
execute the operation.
158
The placement of a precondition in the UML metamodel is shown in Figure 31. The following well-formedness rule must
hold. This rule also defines the value of the contextual Classifier.
M o d e lE le m e n t
(fro m C o re )
0 ..n
+ c o n s tr a i n t
+ c o n s tra i n e d E le m e n t
{o rd e re d }
+ o w ne r
0 ..n
C l a s s i fi e r
(fro m C o re )+ fe a tu re
0 ..1 (fro m C o re )
F e a tu re
B e h a vi o ra lF e a tu re
0 ..n
C o n s tra i nt
(fro m C o re )
0 ..1
1
+body
E xp re s s i o n
(f rom D a t a Ty p e s )
1
E xp re s s i o n In O c l
(fro m C o re )
O c lE x pr es s io n
+ b o d yE xp re s s i o n
Figure 31 - An OCL ExpressionInOcl used as a pre- or post-condition.
[1] The Constraint has the stereotype <<precondition>> (A), and is attached to only one model element (B), and to a BehavioralFeature (C), which has an owner (D). The contextual classifier is the owner of the operation to which the constraint is
attached, and the type of the OCL expression must be Boolean
context Expression
inv: self.constraint.stereotype.name = ’precondition’
-- A
and
-- B
and
self.constraint.constrainedElement->any(true).oclIsKindOf(BehavioralFeature)
and
self.constraint.constrainedElement->any(true)
-- D
.oclAsType(BehavioralFeature).owner->size() = 1
implies
.oclAsType(BehavioralFeature).owner
and
-- C
[2] Inside a precondtion constraint the use of @pre is not allowed.
inv: --
12.8
Postcondition
Like a precondition, a postcondition is a constraint that may be linked to an Operation of a Classifier. The purpose of a
postcondition is to specify the conditions that must hold after the operation executes. A postcondition consists of an OCL
expression of type Boolean. The expression must evaluate to true at the moment that the operation stops executing, but
159
only for the instance that has just executed the operation. Within an OCL expression used in a postcondition, the "@pre"
mark can be used to refer to values at precondition time. The variable result refers to the return value of the operation if
there is any.
The placement of a postcondition in the UML metamodel is equal to the placement of a precondition, which is shown in
Figure 31. The following well-formedness rule must hold. This rule also defines the value of the contextual Classifier.
[1] The Constraint has the stereotype <<postcondition>> (A), and it is attached to only one model element (B), that is an
BehavioralFeature (C), which has an owner (D). The contextual classifier is the owner of the operation to which the constraint is attached, and the type of the OCL expression must be Boolean
context Expression
inv: self.constraint.stereotype.name = ’postcondition’
-- A
and
-- B
and
self.constraint.constrainedElement->any(true).oclIsKindOf(BehavioralFeature) -- C
and
-- D
.oclAsType(BehavioralFeature).owner->size() = 1
implies
self.constraint.constrainedElement->any().oclAsType(BehavioralFeature).owner
and
12.9
Initial value expression
An initial value expression is an expression that may be linked to an Attribute of a Classifier, or to an AssociationEnd. An
OCL expression acting as the initial value of an attribute must conform to the defined type of the attribute. An OCL
expression acting as the initial value of an association end must conform to the type of the association end, i.e. the type
of the attached Classifier when the multiplicity is maximum one, or OrderedSet with element type the type of the attached
Classifier when the multiplicity is maximum more than one.
The OCL expression is evaluated at the creation time of the instance that owns the attribute for this created instance in the
case of an inital value for an attribute. In the case of an inital value for an association end, the OCL expression is
evaluated at the creation time of the instance of the Classifier at the other end(s) of the association.
The placement of an attribute initial value in the UML metamodel is shown in Figure 32. The following well-formedness
rule must hold. This rule also defines the value of the contextual Classifier.
Note – The placement of an intial value of an association end is dependent upon the UML 2.0 metamodel. So are the wellformedness rules for this case.
[1] The Expression is the initial value of an attribute (A), and the Attribute has an owner (B). The contextual classifier is the
owner of the attribute, and the type of the OCL expression must conform to the type of the attribute.
inv: self.attribute->notEmpty()
and
160
-- A
+ fea ture
(from Core) 0..n
{ordered}
F eature
+ ow ner
C lassifier
0..1
(from Core)
1 +type
S tructuralFea ture
(from Core)
0 ..n
0..1
E xpression
A ttribute +attribute
0..1 +initialV alue (from DataTy pes )
(from Core)
E xp re ssionInOcl
+ bo dyE xpression OclE xpression
1
Figure 32 - Expression used to define the inital value of an attribute
self.attribute.owner->size() = 1
-- B
implies
contextualClassifier = self.attribute.owner
and
self.bodyExpression.type.conformsTo(self.attribute.type)
[2] Inside an initial attribute value the use of @pre is not allowed.
inv: -- TBD
12.10 Derived value expression
A derived value expressionis an expression that may be linked to to an Attribute of a Classifier, or to an AssociationEnd.
An OCL expression acting as the derived value of an attribute must conform to the defined type of the attribute. An OCL
expression acting as the derived value of an association end must conform to the type of the association end, i.e. the type
of the attached Classifier when the multiplicity is maximum one, or OrderedSet with element type the type of the attached
Classifier when the multiplicity is maximum more than one.
A derived value expression is an invariant that states that the value of the attribute or association end must always be
equal to the value obtained from evaluating the expression.
Note – The placement of a derived value expression is dependent upon the UML 2.0 metamodel. So are the well-formedness
rules for this case.
12.11 Operation body expression
A body expression is an expression that may be linked to to an Operation of a Classifier, that is marked Query operation.
An OCL expression acting as the body of an operation must conform to the result type of the operation. Evaluating the
body expression gives the result of the operation at a certain point in time.
161
ModelElement
Classifier
(from Core)
(from Core)
+context
OclExpression
0..1
+bodyExpression
0..n +behavior
StateMachine
1
(from State Machines)
0..1
0..n
+statemachine
ExpressionInOcl
+transitions
+state
State
0..n
(from State Machines) +internalTransition
0 ..1
1
+transition
Transition
+guard
0..1
Guard
0..1
+guard
+expression
Expre ssion
1
(from DataTypes)
Figure 33 - An OCL expression used as a Guard expression
Note – The placement of an operation body expression is dependent upon the UML 2.0 metamodel. So are the well-formedness rules for this case.
12.12 Guard
A guard is an expression that may be linked to a Transition in a StateMachine. An OCL expression acting as the guard of
a transition restricts the transition. An OCL expression acting as value of a guard is of type Boolean. The expresion is
evaluated at the moment that the transition attached to the guard is attempted.
The placement of a guard in the UML metamodel is shown in Figure 33. The following well-formedness rule must hold.
In order to state the rule a number of additional operations are defined. The rule also defines the value of the contextual
Classifier.
[1] The statemachine in which the guard appears must have a context (A), that is a Classifier (B). The contextual classifier is
the owner of the statemachine, and the type of the OCL expression must be Boolean.
inv: not self.guard.transition.getStateMachine().context.oclIsUndefined()
and
self.guard.transition.getStateMachine().context.oclIsKindOf(Classifier)
implies
162
-- A
-- B
self.guard.transition.getStateMachine().context.oclAsType(Classifier)
and
[2] Inside an guard the use of @pre is not allowed.
inv: --
12.13 Concrete Syntax of Context Declarations
This section describes the concrete syntax for specifying the context of the different types of usage of OCL expressions.
It makes use of grammar rules defined in Chapter 9 (“Concrete Syntax”). Here too, every production rule is associated to
the abstract syntax by the type of the attribute ast. However, we must sometimes refer to the abstract syntax of the UML
to find the right type for each production.
Visibility rules etc. must be defined in the UML metamodel. Here we assume that every classifier has an operation
visibleElements(), which returns an instance of type Environment, as defined in chapter 9 (“Concrete Syntax”).
Note – The context declarations as described in this section are not needed when the OCL expressions are attached directly to
the UML model. This concerete syntax for context declarations is only there to facilitate separate OCl expressions in text files.
Because of the assumption that the concrete syntax below is used separate from the UML model, we assume the existence
of an operation getClassifier() on the UML model that allows us to find a Classifier anywhere in the corresponding
model. The signature of this operation is defined as follows:
context Model::findClassifier( pathName : Sequence(String) ) : Classifier
The pathName needs not be a fully qualified name (it may be), as long as it can uniquely identify the classifier
siomewhere in the UML model. If a classifier name occurs more than once, it needs to be qualified with its owning
package (recusiveley) until the qualified name is unique. If more than one classifier is found, the operation returns
OclUndefined. The variable Model is used to refer to the UML Model. It is used as Model.findClassifier().
Likewise, we assume the existence of an operation getPackage() on the UML model that allows us to find a Package
anywhere in the corresponding model. The signature of this operation is defined as follows:
context Model::findPackage( pathName : Sequence(String) ) : Package
In this case the pathName needs be a fully qualified name.
Note – The rules for the synthesized and inherited attributes associated with the grammar all depend upon the UML 2.0 metamodel. They cannot be written until this metamodel has been stablelized. Therefore only the grammar rules are given.
12.13.1 packageDeclarationCS
This production rule represents a package declaration.
[A] packageDeclarationCS ::= ’package’ pathNameCS contextDeclCS*
’endpackage’
[B] packageDeclarationCS ::= contextDeclCS*
12.13.2 contextDeclarationCS
This production rule represents all different context declarations.
[A] contextDeclarationCS ::= attrOrAssocContextCS
163
[C] contextDeclarationCS ::= classifierContextDeclCS
[D] contextDeclarationCS ::= operationContextDeclCS
12.13.3 attrOrAssocContextCS
This production rule represents a context declaration for expressions that can be coupled to an attribute or association end.
The path name refers to the "owner" of the attribute or association end, the simple name refers to its name, the type states
its type.
attrOrAssocContextCS ::= ’context’ pathNameCS ’::’ simpleName’:’ typeCS
initOrDerValueCS
12.13.4 initOrDerValueCS
This production rule represents an initial or derived value expression.
[A] initOrDerValueCS[1] ::= ’init’ ’:’ OclExpression
initOrDerValueCS[2]?
[B] initOrDerValueCS[1] ::= ’derive’ ’:’ OclExpression
initOrDerValueCS[2]?
12.13.5 classifierContextDeclCS
This production rule represents a context declaration for expressions that can be coupled to classifiers.
classifierContextDeclCS ::= ’context’ pathNameCS invOrDefCS
12.13.6 invOrDefCS
This production rule represents an invariant or definition.
[A] invOrDefCS[1] ::= ’inv’ (simpleNameCS)? ’:’ OclExpressionCS
invOrDefCS[2]
[B] invOrDefCS[1] ::= ’def’ (simpleNameCS)? ’:’ defExpressionCS
invOrDefCS[2]
12.13.7 defExpressionCS
This production rule represents a definition expression. The defExpressionCS nonterminal has the purpose of defining
additional attributes or operations in OCL. They map directly to a UML attribute or operation with a constraint that
defines the derivation of the attribute or operation result value. Note that VariableDeclarationCS has been defined in
Chapter 9.
[A] defExpressionCS ::= VariableDeclarationCS ’=’ OclExpression
[B] defExpressionCS ::= operationCS ’=’ OclExpression
12.13.8 operationContextDeclCS
This production rule represents a context declaration for expressions that can be coupled to an operation.
164
operationContextDeclCS ::= ’context’ operationCS prePostOrBodyDeclCS
12.13.9 prePostOrBodyDeclCS
This production rule represents a pre- or postcondition or body expression.
[A] prePostOrBodyDeclCS[1] ::= ’pre’ (simpleNameCS)? ’:’ OclExpressionCS
prePostOrBodyDeclCS[2]?
[B] prePostOrBodyDeclCS[1] ::= ’post’ (simpleNameCS)? ’:’ OclExpressionCS
[C] prePostOrBodyDeclCS[1] ::= ’body’ (simpleNameCS)? ’:’ OclExpressionCS
12.13.10 operationCS
This production rule represents an operation in a context declaration or definition expression.
[A] operationCS ::= pathNameCS ’::’ simpleNameCS ’(’ parametersCS? ’)’ ’:’
typeCS?
[B] operationCS ::= simpleNameCS ’(’ parametersCS? ’)’ ’:’ typeCS?
12.13.11 parametersCS
This production rule represents the formal parameters of an operation .
parametersCS[1] ::= VariableDeclarationCS (’,’ parametersCS[2] )?
165
166
13
Alignment of OCL, UML and MOF Metamodels
This section describes the connections between the OCL and UML metamodels.
13.1
Introduction
This chapter provides the neccesary information to align the OCL and UML 2.0 metamodels. It is meant to be a useful
reference to the dependencies between the UML and OCL documents that make part of the UML 2.0 standard.
All references made to metaclasses in the UML 1.4 metamodel that are used in the current definition of the abstract
syntax of OCL (in chapter 8) are listed. These or similar metaclasses are expected to be part of the UML 2.0 metamodel.
The references need to be aligned with the UML 2.0 metamodel as soon as that metamodel is stable.
As described in Section 2 “Conformance,” on page 1 the OCL specification will define a subset that is MOF compliant,
while the complete specification is UML compliant. Because the MOF 2.0 Core and the UML 2.0 Infrastructure are
devleoped in parallel with this OCL 2.0 submission, the exact MOF compliant subset of OCL cannot be defined in this
document. This needs to be done during alignment when all submission are stable.
Another issue in alignment is where in a model OCL expressions may be used. These placements are governed by the
references made in the UML 2.0 metamodel to the metaclasses Expression, Constraint, and similar metaclasses. In
Chapter 12 a number of placements in the model where OCL expressions can be useful, have been described, but others
may be added. The UML 2.0 metamodel should provide a way to link to an OCL expression in these cases. This chapter
lists the contexts already foreseen, and indicates the expectations on the UML 2.0 metamodel in each case.
Finally, this chapter lists a number of aspects of the UML 2.0 metamodel that are not required but convenient in the
specification of OCL.
13.2
Use of the UML Metamodel
The metaclasses from the UML 1.4 metamodel that are listed in Table 6, are referenced in the abstract syntax of this
submission. These or similar classes are expected to be part of the UML 2.0 metamodel. The list is divided into classes
that should be present in a core metamodel, and metaclasses that should be present in an extension to this core that deals
with states and messaging. Preferably the core metaclasses are present in the infrastructure of UML, and in the core of the
MOF.
Potentially there is an overlap between the UML 2.0 infrastructure submissions and this submission in the definition of
literal expressions. A final issue is that this submission would be helped if there is a way in the UML to define template
classes. This feature is used in the definition of the OCL standard library to define collection types..
Table 6 - Overview of UML 1.4. metaclasses used in this submission
Metaclass
Expected in
MOF and UML
AssociationClass
Expected in UML
Needed for state and
message values
Assumptions
X
AssociationEnd
X
Attribute
X
Classifier
X
167
Table 6 - Overview of UML 1.4. metaclasses used in this submission
Metaclass
Expected in
MOF and UML
DataType
X
Enumeration
X
EnumLiteral
X
ModelElement
X
Primitive
X
StructuralFeature
X
Operation
X
Expected in UML
Needed for state and
message values
Assumptions
X
Operations have Parameters
and each parameter has a
direction kind (ParameterDirectionKind).
CallAction
X
SendAction
X
Signal
X
13.3
Signals have attributes.
Use of the OCL metamodel in the UML metamodel
OCL expressions can be used anywhere in the model where a value needs to be specified. Table 7 lists a number of places
in a model, where we expect OCL expressions will be useful. This list is not exhaustive, other uses of OCL expressions
can be added. For some cases this submission defines a special concrete syntax, in case the OCL expression is added to
the model not in a diagram, but in another (text) file. The UML 2.0 metamodel needs to link the mentioned metaclasses
in some manner to the metaclass Expression, or to another metaclass suitable to hold an OCL expression.
Table 7 - Overview of places in a model where an OCL expression may be used
Related UML
metaclasses
Function of
expression
Concrete syntax defined in
OCL 2.0 submission
Attribute
inital value
X
Attribute
derivation rule
X
AssociationEnd
inital value
X
AssociationEnd
derivation rule
X
Classifier
invariant
X
Classifier, Attribute
definition of new
attribute
X
Classifier, Operation
definition of new
operation
X
168
Table 7 - Overview of places in a model where an OCL expression may be used
Related UML
metaclasses
Function of
expression
Concrete syntax defined in
OCL 2.0 submission
Operation
precondition
X
Operation
postcondition
X
Operation
body expression
X
AssociationEnd
value of multiplicity
Guard
specification of
condition
Message
specification of source
Message
specification of target
Message
specification of
condition
Message
actual parameter value
Action
specification of target
Action
actual parameter value
Change Event
condition
Use Case
precondition
Use Case
postcondition
13.4
Wishlist
This section lists a number of items that would be convenient for this submission, if present in the UML 2.0 metamodel.
1.
It would be convenient if there is a way to learn from a Classifier whether it uses value identity or reference identity.
2.
This submission defines a number of additional operations to metaclasses in the UML 1.4 metamodel. It would be
convenient if the UML 2.0 metamodel would provide those operations, specially they appear to be useful in other
submissions, like the Superstructure submission. In this submission the following additional operations are defined
on Classifier:
• commonSuperType: results in the most specific common supertype of two classifiers
• lookupAttribute
• lookupAssociationEnd
• lookupAssociationClass
• lookupOperation
• lookupSignal
• allRecptions
169
• On Operation:
•hasMatchingSignature
• On Parameter:
•asAttribute
•make
• On Signal
•hasMatchingSignature
• On State and on Transition:
•getStateMachine
170
S EMANTICS
A
S EMANTICS
This section formally defines the syntax and semantics of OCL. Most of the material in this section is based on
work presented in [Ric02]. This section is organized as follows. Section A.1 defines the concept of object models.
Object models provide information used as context for OCL expressions and constraints. Section A.2 defines the
type system of OCL and the set of standard operations. Finally, Section A.3 defines the syntax and semantics of
OCL expressions.
A.1
O BJECT M ODELS
In this section, the notion of an object model is formally defined. An object model provides the context for OCL
expressions and constraints. A precise understanding of object models is required before a formal definition of
OCL expressions can be given. Section A.1.1 proceeds with a formal definition of the syntax of object models.
The semantics of object models is defined in Section A.1.2. This section also defines the notion of system states
as snapshots of a running system.
A.1.1
S YNTAX OF O BJECT M ODELS
In this section, we formally define the syntax of object models. Such a model has the following components:
• a set of classes,
• a set of attributes for each class,
• a set of operations for each class,
• a set of associations with role names and multiplicities,
• a generalization hierarchy over classes.
Additionally, types such as Integer, String, Set(Real) are available for describing types of attributes and operation
parameters. In the following, each of the model components is considered in detail. The following definitions are
combined in Section A.1.1.7 to give a complete definition of the syntax of object models. For naming model components, we assume in this section an alphabet A and a set of finite, non-empty names N ⊆ A+ over alphabet A
to be given.
A.1.1.1
T YPES
Types are considered in depth in Section A.2. For now, we assume that there is a signature Σ = (T, Ω) with T
being a set of type names, and Ω being a set of operations over types in T . The set T includes the basic types
Integer, Real, Boolean, and String. These are the predefined basic types of OCL. All type domains include an
undefined value that allows to operate with unknown or “null” values. Operations in Ω include, for example, the
usual arithmetic operations +, −, ∗, /, etc. for integers. Furthermore, collection types are available for describing
collections of values, for example, Set(String), Bag(Integer), and Sequence(Real). Structured values are described
by tuple types with named components, for example, Tuple(name:String, age:Integer).
OCL 2.0 R EVISED S UBMISSION
V ERSION 1.5, J UNE 3, 2002
A-1
S EMANTICS
A.1.1.2
C LASSES
The central concept of UML for modeling entities of the problem domain is the class. A class provides a common
description for a set of objects sharing the same properties.
D EFINITION A.1 (C LASSES )
The set of classes is a finite set of names C LASS ⊆ N .
Each class c ∈ C LASS induces an object type tc ∈ T having the same name as the class. A value of an object type
refers to an object of the corresponding class. The main difference between classes and object types is that the
interpretation of the latter includes a special undefined value.
Note that for a definition of the semantics of OCL, UML’s distinction between classes and interfaces does not
matter. OCL specifies constraints for instances of a given interface specification. Whether this specification is
stated in the form of a class or interface definition makes no difference.
A.1.1.3
ATTRIBUTES
Attributes are part of a class declaration in UML. Objects are associated with attribute values describing properties
of the object. An attribute has a name and a type specifying the domain of attribute values.
D EFINITION A.2 (ATTRIBUTES )
Let t ∈ T be a type. The attributes of a class c ∈ C LASS are defined as a set ATTc of signatures a : tc → t where
the attribute name a is an element of N , and tc ∈ T is the type of class c.
All attributes of a class have distinct names. In particular, an attribute name may not be used again to define another
attribute with a different type.
∀t, t0 ∈ T : (a : tc → t ∈ ATTc and a : tc → t0 ∈ ATTc ) =⇒ t = t0
Attributes with the same name may, however, appear in different classes that are not related by generalization.
Details are given in Section A.1.1.6 where we discuss generalization. The set of attribute names and class names
need not be disjoint.
A.1.1.4
O PERATIONS
Operations are part of a class definition. They are used to describe behavioral properties of objects. The effect of an
operation may be specified in a declarative way with OCL pre- and postconditions. Section A.3 discusses pre- and
postconditions in detail. Furthermore, operations performing computations without side effects can be specified
with OCL. In this case, the computation is determined by an explicit OCL expression. This is also discussed
in Section A.3. Here, we focus on the syntax of operation signatures declaring the interface of user-defined
operations. In contrast, other kinds of operations which are not explicitly defined by a modeler are, for example,
navigation operations derived from associations. These are discussed in the next section and in Section A.2.
D EFINITION A.3 (O PERATIONS )
Let t and t1 , . . . , tn be types in T . Operations of a class c ∈ C LASS with type tc ∈ T are defined by a set O Pc of
signatures ω : tc × t1 × · · · × tn → t with operation symbols ω being elements of N .
The name of an operation is determined by the symbol ω. The first parameter tc denotes the type of the class
instance to which the operation is applied. An operation may have any number of parameters but only a single
return type. In general, UML allows multiple return values. We currently do not support this feature in OCL.
A-2
S EMANTICS
A.1.1.5
A SSOCIATIONS
Associations describe structural relationships between classes. Generally, classes may participate in any number
of associations, and associations may connect two or more classes.
D EFINITION A.4 (A SSOCIATIONS )
The set of associations is given by
i. a finite set of names A SSOC ⊆ N ,
(
A SSOC → C LASS+
ii. a function associates :
as 7→ hc1 , . . . , cn i with (n ≥ 2)
.
The function associates maps each association name as ∈ A SSOC to a finite list hc1 , . . . , cn i of classes participating in the association. The number n of participating classes is also called the degree of an association; associations
with degree n are called n-ary associations. For many problems the use of binary associations is often sufficient.
A self-association (or recursive association) sa is a binary association where both ends of the association are attached to the same class c such that associates(sa) = hc, ci. The function associates does not have to be injective.
Multiple associations over the same set of classes are possible.
R OLE
NAMES
Classes may appear more than once in an association each time playing a different role. For example, in a selfassociation PhoneCall on a class Person we need to distinguish between the person having the role of a caller and
another person being the callee. Therefore we assign each class participating in an association a unique role name.
Role names are also important for OCL navigation expressions. A role name of a class is used to determine the
navigation path in this kind of expressions.
D EFINITION A.5 (ROLE NAMES )
Let as ∈ A SSOC be an association with associates(as) = hc1 , . . . , cn i. Role names for an association are defined
by a function
(
A SSOC → N +
roles :
as 7→ hr1 , . . . , rn i with (n ≥ 2)
where all role names must be distinct, i.e.,
∀i, j ∈ {1, . . . , n} : i 6= j =⇒ ri 6= rj .
The function roles(as) = hr1 , . . . , rn i assigns each class ci for 1 ≤ i ≤ n participating in the association a unique
role name ri . If role names are omitted in a class diagram, implicit names are constructed in UML by using the
name of the class at the target end and changing its first letter to lower case. As mentioned above, explicit role
names are mandatory for self-associations.
A-3
S EMANTICS
Additional syntactical constraints are required for ensuring the uniqueness of role names when a class is part of
many associations. We first define a function participating that gives the set of associations a class participates
in.


C LASS → P(A SSOC)
participating : c 7→ {as | as ∈ A SSOC ∧ associates(as) = hc1 , . . . , cn i


∧ ∃i ∈ {1, . . . , n} : ci = c}
The following function navends gives the set of all role names reachable (or navigable) from a class over a given
association.

C LASS × A SSOC → P(N )



 (c, as) 7→ {r | associates(as) = hc , . . . , c i
1
n
navends :

∧ roles(as) = hr1 , . . . , rn i



∧ ∃i, j ∈ {1, . . . , n} : (i 6= j ∧ ci = c ∧ rj = r)}
The set of role names that are reachable from a class along all associations the class participates in can then be
determined by the following function.
(
C LASS → P(N )
navends(c) :
S
c 7→ as∈participating(c) navends(c, as)
M ULTIPLICITIES
An association specifies the possible existence of links between objects of associated classes. The number of links
that an object can be part of is specified with multiplicities. A multiplicity specification in UML can be represented
by a set of natural numbers.
D EFINITION A.6 (M ULTIPLICITIES )
Let as ∈ A SSOC be an association with associates(as) = hc1 , . . . , cn i. The function multiplicities(as) =
hM1 , . . . , Mn i assigns each class ci participating in the association a non-empty set Mi ⊆ N0 with Mi 6= {0} for
all 1 ≤ i ≤ n.
The precise meaning of multiplicities is defined as part of the interpretation of object models in Section A.1.2.
R EMARK :
AGGREGATION AND COMPOSITION
Special forms of associations are aggregation and composition. In general, aggregations and compositions impose
additional restrictions on relationships. An aggregation is a special kind of binary association representing a partof relationship. The aggregate is marked with a hollow diamond at the association end in class diagrams. An
aggregation implies the constraint that an object cannot be part of itself. Therefore, a link of an aggregation may
not connect the same object. In case of chained aggregations, the chain may not contain cycles.
An even stronger form of aggregation is composition. The composite is marked with a filled diamond at the
association end in class diagrams. In addition to the requirements for aggregations, a part may only belong to at
most one composite.
These seemingly simple concepts can have quite complex semantic issues [AFGP96, Mot96, Pri97, GR99, HSB99,
BHS99, BHSOG01]. Here, we are concerned only with syntax. The syntax of aggregations and compositions is
very similar to associations. Therefore, we do not add an extra concept to our formalism. As a convention,
we always use the first component in an association for a class playing the role of an aggregate or composite.
The semantic restrictions then have to be expressed as an explicit constraint. A systematic way for mapping
aggregations and compositions to simple associations plus OCL constraints is presented in [GR99].
A-4
S EMANTICS
A.1.1.6
G ENERALIZATION
A generalization is a taxonomic relationship between two classes. This relationship specializes a general class into
a more specific class. Specialization and generalization are different views of the same concept. Generalization
relationships form a hierarchy over the set of classes.
D EFINITION A.7 (G ENERALIZATION HIERARCHY )
A generalization hierarchy ≺ is a partial order on the set of classes C LASS.
Pairs in ≺ describe generalization relationships between two classes. For classes c1 , c2 ∈ C LASS with c1 ≺ c2 ,
the class c1 is called a child class of c2 , and c2 is called a parent class of c1 .
F ULL
DESCRIPTOR OF A CLASS
A child class implicitly inherits attributes, operations and associations of its parent classes. The set of properties
defined in a class together with its inherited properties is called a full descriptor in UML. We can formalize the
full descriptor in our framework as follows. First, we define a convenience function for collecting all parents of a
given class.
(
C LASS → P(C LASS)
parents :
c 7→ {c0 | c0 ∈ C LASS ∧ c ≺ c0 }
The full set of attributes of class c is the set ATT∗c containing all inherited attributes and those that are defined
directly in the class.
[
ATT∗c = ATTc ∪
ATTc0
c0 ∈parents(c)
We define the set of inherited user-defined operations analogously.
[
O P∗c = O Pc ∪
O P c0
c0 ∈parents(c)
Finally, the set of navigable role names for a class and all of its parents is given as follows.
[
navends∗ (c) = navends(c) ∪
navends(c0 )
c0 ∈parents(c)
D EFINITION A.8 (F ULL DESCRIPTOR OF A CLASS )
The full descriptor of a class c ∈ C LASS is a structure FDc = (ATT∗c , O P∗c , navends∗ (c)) containing all attributes,
user-defined operations, and navigable role names defined for the class and all of its parents.
The UML standard requires that properties of a full descriptor must be distinct. For example, a class may not
define an attribute that is already defined in one of its parent classes. These constraints are captured more precisely
by the following well-formedness rules in our framework. Each constraint must hold for each class c ∈ C LASS.
1. Attributes are defined in exactly one class.
∀(a : tc → t, a0 : tc0 → t0 ∈ ATT∗c ) :
(a = a0 =⇒ tc = tc0 ∧ t = t0 )
(WF-1)
A-5
S EMANTICS
2. In a full class descriptor, an operation may only be defined once. The first parameter of an operation signature
indicates the class in which the operation is defined. The following condition guarantees that each operation
in a full class descriptor is defined in a single class.
∀(ω : tc × t1 × · · · × tn → t, ω : tc0 × t1 × · · · × tn → t0 ∈ O P∗c ) :
(tc = tc0 )
(WF-2)
3. Role names are defined in exactly one class.
∀c1 , c2 ∈ parents(c) ∪ {c} :
(c1 6= c2 =⇒ navends(c1 ) ∩ navends(c2 ) = ∅)
(WF-3)
4. Attribute names and role names must not conflict. This is necessary because in OCL the same notation is
used for attribute access and navigation by role name. For example, the expression self.x may either be
a reference to an attribute x or a reference to a role name x.
∀(a : tc → t ∈ ATT∗c ) : ∀r ∈ navends∗ (c) :
(a 6= r)
(WF-4)
Note that operations may have the same name as attributes or role names because the concrete syntax of OCL
allows us to distinguish between these cases. For example, the expression self.age is either an attribute or role
name reference, but a call to an operation age without parameters is written as self.age().
A.1.1.7
F ORMAL S YNTAX
We combine the components introduced in the previous section to formally define the syntax of object models.
D EFINITION A.9 (S YNTAX OF OBJECT MODELS )
The syntax of an object model is a structure
M = (C LASS, ATTc , O Pc , A SSOC, associates, roles, multiplicities, ≺)
where
i. C LASS is a set of classes (Definition A.1).
ii. ATTc is a set of operation signatures for functions mapping an object of class c to an associated attribute
value (Definition A.2).
iii. O Pc is a set of signatures for user-defined operations of a class c (Definition A.3).
iv. A SSOC is a set of association names (Definition A.4).
(a) associates is a function mapping each association name to a list of participating classes
(Definition A.4).
(b) roles is a function assigning each end of an association a role name (Definition A.5).
(c) multiplicities is a function assigning each end of an association a multiplicity specification
(Definition A.6).
v. ≺ is a partial order on C LASS reflecting the generalization hierarchy of classes (Definitions A.7 and A.8).
A-6
S EMANTICS
A.1.2
I NTERPRETATION OF O BJECT M ODELS
In the previous section, the syntax of object models has been defined. An interpretation of object models is
presented in the following.
A.1.2.1
O BJECTS
The domain of a class c ∈ C LASS is the set of objects that can be created by this class and all of its child classes.
Objects are referred to by unique object identifiers. In the following, we will make no conceptual distinction
between objects and their identifiers. Each object is uniquely determined by its identifier and vice versa. Therefore,
the actual representation of an object is not important for our purposes.
D EFINITION A.10 (O BJECT IDENTIFIERS )
i. The set of object identifiers of a class c ∈ C LASS is defined by an infinite set oid(c) = {c1 , c2 , . . . }.
S
ii. The domain of a class c ∈ C LASS is defined as IC LASS (c) = {oid(c0 ) | c0 ∈ C LASS ∧ c0 c}.
In the following, we will omit the index for a mapping I when the context is obvious. The concrete scheme for
naming objects is not important as long as every object can be uniquely identified, i.e., there are no different objects
having the same name. We sometimes use single letters combined with increasing indexes to name objects if it is
clear from the context to which class these objects belong.
G ENERALIZATION
The above definition implies that a generalization hierarchy induces a subset relation on the semantic domain of
classes. The set of object identifiers of a child class is a subset of the set of object identifiers of its parent classes.
With other words, we have
∀c1 , c2 ∈ C LASS : c1 ≺ c2 =⇒ I(c1 ) ⊆ I(c2 ) .
From the perspective of programming languages this closely corresponds to the domain-inclusion semantics commonly associated with subtyping and inheritance [CW85]. Data models for object-oriented databases such as the
generic OODB model presented in [AHV95] also assume an inclusion semantics for class extensions. This requirement guarantees two fundamental properties of generalizations. First, an object of a child class has (inherits)
all the properties of its parent classes because it is an instance of the parent classes. Second, this implies that an
object of a more specialized class can be used anywhere where an object of a more general class is expected (principle of substitutability) because it has at least all the properties of the parent classes. In general, the interpretation
of classes is pairwise disjoint if two classifiers are not related by generalization and do not have a common child.
A.1.2.2
L INKS
An association describes possible connections between objects of the classes participating in the association. A
connection is also called a link in UML terminology. The interpretation of an association is a relation describing
the set of all possible links between objects of the associated classes and their children.
A-7
S EMANTICS
D EFINITION A.11 (L INKS )
Each association as ∈ A SSOC with associates(as) = hc1 , . . . , cn i is interpreted as the Cartesian product of the
sets of object identifiers of the participating classes: IA SSOC (as) = IC LASS (c1 ) × · · · × IC LASS (cn ). A link denoting
a connection between objects is an element las ∈ IA SSOC (as).
A.1.2.3
S YSTEM S TATE
Objects, links and attribute values constitute the state of a system at a particular moment in time. A system is in
different states as it changes over time. Therefore, a system state is also called a snapshot of a running system.
With respect to OCL, we can in many cases concentrate on a single system state given at a discrete point in time.
For example, a system state provides the complete context for the evaluation of OCL invariants. For pre- and
postconditions, however, it is necessary to consider two consecutive states.
D EFINITION A.12 (S YSTEM STATE )
A system state for a model M is a structure σ(M) = (σC LASS , σATT , σA SSOC ).
i. The finite sets σC LASS (c) contain all objects of a class c ∈ C LASS existing in the system state:
σC LASS (c) ⊂ oid(c).
ii. Functions σATT assign attribute values to each object: σATT (a) : σC LASS (c) → I(t) for each
a : tc → t ∈ ATT∗c .
iii. The finite sets σA SSOC contain links connecting objects. For each as ∈ A SSOC: σA SSOC (as) ⊂ IA SSOC (as).
A link set must satisfy all multiplicity specifications defined for an association (the function πi (l) projects
the ith component of a tuple or list l, whereas the function π̄i (l) projects all but the ith component):
∀i ∈ {1, . . . , n}, ∀l ∈ σA SSOC (as) :
0
0
|{l | l ∈ σA SSOC (as) ∧ (π̄i (l0 ) = π̄i (l))}| ∈ πi (multiplicities(as))
A-8
S EMANTICS
A.2
OCL T YPES AND O PERATIONS
OCL is a strongly typed language. A type is assigned to every OCL expression and typing rules determine in
which ways well-formed expressions can be constructed. In addition to those types introduced by UML models,
there are a number of predefined OCL types and operations available for use with any UML model. This section
formally defines the type system of OCL. Types and their domains are fixed, and the abstract syntax and semantics
of operations is defined.
Our general approach to defining the type system is as follows. Types are associated with a set of operations.
These operations describe functions combining or operating on values of the type domains. In our approach, we
use a data signature Σ = (T, Ω) to describe the syntax of types and operations. The semantics of types in T
and operations in Ω is defined by a mapping that assigns each type a domain and each operation a function. The
definition of the syntax and semantics of types and operations will be developed and extended in several steps. At
the end of this section, the complete set of types is defined in a single data signature.
Section A.2.1 defines the basic types Integer, Real, Boolean and String. Enumeration types are defined in Section A.2.3. Section A.2.4 introduces object types that correspond to classes in a model. Collection and tuple
types are discussed in Section A.2.5. The special types OclAny and OclState are considered in Section A.2.6.
Section A.2.7 introduces subtype relationships forming a type hierarchy. All types and operations are finally
summarized in a data signature defined in Section A.2.8.
A.2.1
BASIC T YPES
Basic types are Integer, Real, Boolean and String. The syntax of basic types and their operations is defined by a
signature ΣB = (TB , ΩB ). TB is the set of basic types, ΩB is the set of signatures describing operations over basic
types.
D EFINITION A.13 (S YNTAX OF BASIC TYPES )
The set of basic types TB is defined as TB = {Integer, Real, Boolean, String}.
Next we define the semantics of basic types by mapping each type to a domain.
D EFINITION A.14 (S EMANTICS OF BASIC TYPES )
Let A∗ be the set of finite sequences of characters from a finite alphabet A. The semantics of a basic type t ∈ TB
is a function I mapping each type to a set:
• I(Integer) = Z ∪ {⊥}
• I(Real) = R ∪ {⊥}
• I(Boolean) = {true, false} ∪ {⊥}
• I(String) = A∗ ∪ {⊥}.
The basic type Integer represents the set of integers, Real the set of real numbers, Boolean the truth values true
and false, and String all finite strings over a given alphabet. Each domain also contains a special undefined value
which is motivated in the next section.
A-9
S EMANTICS
A.2.1.1
E RROR H ANDLING
Each domain of a basic type t contains a special value ⊥. This value represents an undefined value which is useful
for two purposes.
1. An undefined value may, for example, be assigned to an attribute of an object. In this case the undefined value
helps to model the situation where the attribute value is not yet known (for example, the email address of a
customer is unknown at the time of the first contact, but will be added later) or does not apply to this specific
object instance (e.g., the customer does not have an email address). This usage of undefined values is wellknown in database modeling and querying with SQL [Dat90, EN94]), in the Extended ER-Model [Gog94],
and in the object specification language TROLL light [Her95].
2. An undefined value can signal an error in the evaluation of an expression. An example for an expression
that is defined by a partial function is the division of integers. The result of a division by zero is undefined.
The problems with partial functions can be eliminated by including an undefined value ⊥ into the domains
of types. For all operations we can then extend their interpretation to total functions.
The interpretation of operations is considered strict unless there is an explicit statement in the following. Hence, an
undefined argument value causes an undefined operation result. This ensures the propagation of error conditions.
A.2.1.2
O PERATIONS
There are a number of predefined operations on basic types. The set ΩB contains the signatures of these operations.
An operation signature describes the name, the parameter types, and the result type of an operation.
D EFINITION A.15 (S YNTAX OF OPERATIONS )
The syntax of an operation is defined by a signature ω : t1 × · · · × tn → t. The signature contains the operation
symbol ω, a list of parameter types t1 , . . . , tn ∈ T , and a result type t ∈ T .
Table A.1 shows a schema defining most predefined operations over basic types. The left column contains partially
parameterized signatures in ΩB . The right column specifies variations for the operation symbols or types in the
left column.
The set of predefined operations includes the usual arithmetic operations +, −, ∗, /, etc. for integers and real
numbers, division (div) and modulo (mod) of integers, sign manipulation (−, abs), conversion of Real values to
Integer values (floor, round), and comparison operations (<, >, ≤, ≥).
Operations for equality and inequality are presented later in Section A.2.2, since they apply to all types. Boolean
values can be combined in different ways (and, or, xor, implies), and they can be negated (not). For strings
the length of a string (size) can be determined, a string can be projected to a substring and two strings can be
concatenated (concat). Finally, assuming a standard alphabet like ASCII or Unicode, case translations are possible
with toUpper and toLower.
Some operation symbols (such as + and −) are overloaded, that is there are signatures having the same operation
symbol but different parameters (concerning number or type) and possibly different result types. Thus in general,
the full argument list has to be considered in order to identify a signature unambiguously.
The operations in Table A.1 all have at least one parameter. There is another set of operations in ΩB which do not
have parameters. These operations are used to produce constant values of basic types. For example, the integer
value 12 can be generated by the operation 12 :→ Integer. Similar operations exist for the other basic types. For
each value, there is an operation with no parameters and an operation symbol that corresponds to the common
notational representation of this value.
A-10
S EMANTICS
Signature
ω : Integer × Integer → Integer
Integer × Real → Real
Real × Integer → Real
Real × Real → Real
ω : Integer × Integer → Integer
/ : t1 × t2 → Real
−:t→t
abs : t → t
floor : t → Integer
round : t → Integer
ω : t1 × t2 → Boolean
ω : Boolean × Boolean → Boolean
not :
size :
concat :
toUpper :
toLower :
substring :
Schema parameters
ω ∈ {+, −, ∗, max, min}
ω ∈ {div, mod}
t1 , t2 ∈ {Integer, Real}
t ∈ {Integer, Real}
ω ∈ {<, >, ≤, ≥},
t1 , t2 ∈ {Integer, Real,
String, Boolean}
ω ∈ {and, or,
xor, implies}
Boolean → Boolean
String → Integer
String × String → String
String → String
String → String
String × Integer × Integer → String
Table A.1: Schema for operations on basic types
A.2.1.3
S EMANTICS
OF
O PERATIONS
D EFINITION A.16 (S EMANTICS OF OPERATIONS )
The semantics of an operation with signature ω : t1 × · · · × tn → t is a total function I(ω : t1 × · · · × tn → t) :
I(t1 ) × · · · × I(tn ) → I(t).
When we refer to an operation, we usually omit the specification of the parameter and result types and only use
the operation symbol if the full signature can be derived from the context.
The next example shows the interpretation of the operation + for adding two integers. The operation has two
arguments i1 , i2 ∈ I(Integer). This example also demonstrates the strict evaluation semantics for undefined
arguments.
(
i1 + i2 if i1 6= ⊥ and i2 6= ⊥,
I(+)(i1 , i2 ) =
⊥
otherwise.
We can define the semantics of the other operations in Table A.1 analogously. The usual semantics of the boolean
operations and, or, xor, implies, and not, is extended for dealing with undefined argument values. Table A.2 shows
the interpretation of boolean operations following the proposal in [CKM+ 99] based on three-valued logic.
Since the semantics of the other basic operations for Integer, Real, and String values is rather obvious, we will not
further elaborate on them here.
A-11
S EMANTICS
b1
false
false
true
true
false
true
⊥
⊥
⊥
b2
false
true
false
true
⊥
⊥
false
true
⊥
b1 and b2
false
false
false
true
false
⊥
false
⊥
⊥
b1 or b2
false
true
true
true
⊥
true
⊥
true
⊥
b1 xor b2
false
true
true
false
⊥
⊥
⊥
⊥
⊥
b1 implies b2
true
true
false
true
true
⊥
⊥
true
⊥
not b1
true
true
false
false
true
false
⊥
⊥
⊥
Table A.2: Semantics of boolean operations
A.2.2
C OMMON O PERATIONS ON ALL T YPES
At this point, we introduce some operations that are defined on all types (including those which are defined in
subsequent sections). The equality of values of the same type can be checked with the operation =t : t × t →
Boolean. Furthermore, the semantics of =t is defined to be strict. For two values v1 , v2 ∈ I(t), we have


true if v1 = v2 , and v1 6= ⊥ and v2 6= ⊥,
I(=t )(v1 , v2 ) = ⊥
if v1 = ⊥ or v2 = ⊥,


false otherwise.
A test for inequality 6=t : t × t → Boolean can be defined analogously. It is also useful to have an operation that
allows to check whether an arbitrary value is well-defined or undefined. This can be done with the operations
isDefinedt : t → Boolean and isUndefinedt : t → Boolean for any type t ∈ T . The semantics of these operations
is given for any v ∈ I(t) by:
I(isDefinedt )(v) = (v 6= ⊥)
I(isUndefinedt )(v) = (v = ⊥)
A.2.3
E NUMERATION T YPES
Enumeration types are user-defined types. An enumeration type is defined by specifying a name and a set of
literals. An enumeration value is one of the literals used for its type definition.
The syntax of enumeration types and their operations is defined by a signature ΣE = (TE , ΩE ). TE is the set of
enumeration types and ΩE the set of signatures describing the operations on enumeration types.
D EFINITION A.17 (S YNTAX OF ENUMERATION TYPES )
An enumeration type t ∈ TE is associated with a finite non-empty set of enumeration literals by a function
literals(t) = {e1t , . . . , ent }.
An enumeration type is interpreted by the set of literals used for its declaration.
D EFINITION A.18 (S EMANTICS OF ENUMERATION TYPES )
The semantics of an enumeration type t ∈ TE is a function I(t) = literals(t) ∪ {⊥}.
A-12
S EMANTICS
A.2.3.1
O PERATIONS
There is only a small number of operations defined on enumeration types: the test for equality or inequality of
two enumeration values. The syntax and semantics of these general operations was defined in Section A.2.2 and
applies to enumeration types as well.
In addition, the operation allInstancest :→ Set(t) is defined for each t ∈ TE to return the set of all literals of the
enumeration:
∀t ∈ TE : I(allInstancest ()) = literals(t)
A.2.4
O BJECT T YPES
A central part of a UML model are classes that describe the structure of objects in a system. For each class, we
define a corresponding object type describing the set of possible object instances. The syntax of object types and
their operations is defined by a signature ΣC = (TC , ΩC ). TC is the set of object types, and ΩC is the set of
signatures describing operations on object types.
D EFINITION A.19 (S YNTAX OF OBJECT TYPES )
Let M be a model with a set C LASS of class names. The set TC of object types is defined such that for each class
c ∈ C LASS there is a type t ∈ TC having the same name as the class c.
We define the following two functions for mapping a class to its type and vice versa.
typeOf : C LASS → TC
classOf : TC → C LASS
The interpretation of classes is used for defining the semantics of object types. The set of object identifiers
IC LASS (c) was introduced in Definition A.10 on page 7.
D EFINITION A.20 (S EMANTICS OF OBJECT TYPES )
The semantics of an object type t ∈ TC with classOf(t) = c is defined as I(t) = IC LASS (c) ∪ {⊥}.
In summary, the domain of an object type is the set of object identifiers defined for the class and its children. The
undefined value that is only available with the type – not the class – allows us to work with values not referring
to any existing object. This is useful, for example, when we have a navigation expression pointing to a class with
multiplicity 0..1. The result of the navigation expression is a value referring to the actual object only if a target
object exists. Otherwise, the result is the undefined value.
A.2.4.1
O PERATIONS
There are four different kinds of operations that are specific to object types.
• Predefined operations: These are operations which are implicitly defined in OCL for all object types.
• Attribute operations: An attribute operation allows access to the attribute value of an object in a given system
state.
A-13
S EMANTICS
• Object operations: A class may have operations that do not have side effects. These operations are marked in
the UML model with the tag isQuery. In general, OCL expressions could be used to define object operations.
The semantics of an object operation is therefore given by the semantics of the associated OCL expression.
• Navigation operations: An object may be connected to other objects via association links. A navigation
expression allows to follow these links and to retrieve connected objects.
P REDEFINED
OPERATIONS
For all classes c ∈ C LASS with object type tc = typeOf(c) the operations
allInstancestc : → Set(tc )
are in ΩC . The semantics is defined as
I(allInstancestc : → Set(tc )) = σC LASS (c) .
This interpretation of allInstances is safe in the sense that its result is always limited to a finite set. The extension
of a class is always a finite set of objects.
ATTRIBUTE
OPERATIONS
Attribute operations are declared in a model specification by the set ATTc for each class c. The set contains
signatures a : tc → t with a being the name of an attribute defined in the class c. The type of the attribute is t. All
attribute operations in ATTc are elements of ΩC . The semantics of an attribute operation is a function mapping an
object identifier to a value of the attribute domain. An attribute value depends on the current system state.
D EFINITION A.21 (S EMANTICS OF ATTRIBUTE OPERATIONS )
An attribute signature a : tc → t in ΩC is interpreted by an attribute value function IATT (a : tc → t) : I(tc ) → I(t)
mapping objects of class c to a value of type t.
(
σATT (a)(c) if c ∈ σC LASS (c),
IATT (a : tc → t)(c) =
⊥
otherwise.
Note that attribute functions are defined for all possible objects. The attempt to access an attribute of a non-existent
object results in an undefined value.
O BJECT
OPERATIONS
Object operations are declared in a model specification. For side effect-free operations the computation can often
be described with an OCL expression. The semantics of a side effect-free object operation can then be given by
the semantics of the OCL expression associated with the operation. We give a semantics for object operations in
Section A.3 when OCL expressions are introduced.
A-14
S EMANTICS
N AVIGATION
OPERATIONS
A fundamental concept of OCL is navigation along associations. Navigation operations start from an object of
a source class and retrieve all connected objects of a target class. In general, every n-ary association induces a
total of n · (n − 1) directed navigation operations, because OCL navigation operations only consider two classes
of an association at a time. For defining the set of navigation operations of a given class, we have to consider all
associations the class is participating in. A corresponding function named participating was defined on page 4.
D EFINITION A.22 (S YNTAX OF NAVIGATION OPERATIONS )
Let M be a model
M = (C LASS, ATTc , O Pc , A SSOC, associates, roles, multiplicities, ≺) .
The set Ωnav (c) of navigation operations for a class c ∈ C LASS is defined such that for each association
as ∈ participating(c) with associates(as) = hc1 , . . . , cn i, roles(as) = hr1 , . . . , rn i, and multiplicities(as) =
hM1 , . . . , Mn i the following signatures are in Ωnav (c).
For all i, j ∈ {1, . . . , n} with i 6= j, ci = c, tci = typeOf(ci ), and tcj = typeOf(cj )
i. if n = 2 and Mj − {0, 1} = ∅ then rj (as,ri ) : tci → tcj ∈ Ωnav (c),
ii. if n > 2 or Mj − {0, 1} =
6 ∅ then rj (as,ri ) : tci → Set(tcj ) ∈ Ωnav (c).
All navigation operations are elements of ΩC .
As discussed in Section A.1, we use unique role names instead of class names for navigation operations in order
to avoid ambiguities. The index of the navigation operation name specifies the association to be navigated along
as well as the source role name of the navigation path. The result type of a navigation over binary associations is
the type of the target class if the multiplicity of the target is given as 0..1 or 1 (i). All other multiplicities allow
an object of the source class to be linked with multiple objects of the target class. Therefore, we need a set type to
represent the navigation result (ii). Non-binary associations always induce set-valued results since a multiplicity
at the target end is interpreted in terms of all source objects. However, for a navigation operation, only a single
source object is considered.
Navigation operations are interpreted by navigation functions. Such a function has the effect of first selecting all
those links of an association where the source object occurs in the link component corresponding to the role of the
source class. The resulting links are then projected onto those objects that correspond to the role of the target class.
D EFINITION A.23 (S EMANTICS OF NAVIGATION OPERATIONS )
The set of objects of class cj linked to an object ci via association as is defined as
L(as)(ci ) = {cj | (c1 , . . . , ci , . . . , cj , . . . , cn ) ∈ σA SSOC (as)}
The semantics of operations in Ωnav (c) is then defined as
i. I(rj (as,ri )
(
cj
: tci → tcj )(ci ) =
⊥
if cj ∈ L(as)(ci ),
otherwise.
ii. I(rj (as,ri ) : tci → Set(tcj ))(ci ) = L(as)(ci ).
A-15
S EMANTICS
A.2.5
C OLLECTION AND T UPLE T YPES
We call a type that allows the aggregation of several values into a single value a complex type. OCL provides
the complex types Set(t), Sequence(t), and Bag(t) for describing collections of values of type t. There is also
a supertype Collection(t) which describes common properties of these types. The OCL collection types are homogeneous in the sense that all elements of a collection must be of the same type t. This restriction is slightly
relaxed by the substitution rule for subtypes in OCL (see Section A.2.7). The rule says that the actual elements of
a collection must have a type which is a subtype of the declared element type. For example, a Set(Person) may
contain elements of type Customer or Employee.
A.2.5.1
S YNTAX
AND
S EMANTICS
Since complex types are parameterized types, we define their syntax recursively by means of type expressions.
D EFINITION A.24 (T YPE EXPRESSIONS )
Let T̂ be a set of types and l1 , . . . , ln ∈ N a set of disjoint names. The set of type expressions TExpr (T̂ ) over T̂ is
defined as follows.
i. If t ∈ T̂ then t ∈ TExpr (T̂ ).
ii. If t ∈ TExpr (T̂ ) then Set(t), Sequence(t), Bag(t) ∈ TExpr (T̂ ).
iii. If t ∈ TExpr (T̂ ) then Collection(t) ∈ TExpr (T̂ ).
iv. If t1 , . . . , tn ∈ TExpr (T̂ ) then Tuple(l1 : t1 , . . . , ln : tn ) ∈ TExpr (T̂ ).
The definition says that every type t ∈ T̂ can be used as an element type for constructing a set, sequence, bag, or
collection type. The components of a tuple type are marked with labels l1 , . . . , ln . Complex types may again be
used as element types for constructing other complex types. The recursive definition allows unlimited nesting of
type expressions.
For the definition of the semantics of type expressions we make the following conventions. Let F(S) denote the
set of all finite subsets of a given set S, S ∗ is the set of all finite sequences over S, and B(S) is the set of all finite
multisets (bags) over S.
D EFINITION A.25 (S EMANTICS OF TYPE EXPRESSIONS )
Let T̂ be a set of types where the domain of each t ∈ T̂ is I(t). The semantics of type expressions TExpr (T̂ ) over
T̂ is defined for all t ∈ T̂ as follows.
i. I(t) is defined as given.
ii. I(Set(t)) = F(I(t)) ∪ {⊥},
I(Sequence(t)) = (I(t))∗ ∪ {⊥},
I(Bag(t)) = B(I(t)) ∪ {⊥}.
iii. I(Collection(t)) = I(Set(t)) ∪ I(Sequence(t)) ∪ I(Bag(t)).
iv. I(Tuple(l1 : t1 , . . . , ln : tn )) = I(t1 ) × · · · × I(tn ) ∪ {⊥}.
A-16
S EMANTICS
In this definition, we observe that the interpretation of the type Collection(t) subsumes the semantics of the set,
sequence and bag type. In OCL, the collection type is described as a supertype of Set(t), Sequence(t) and Bag(t).
This construction greatly simplifies the definition of operations having a similar semantics for each of the concrete
collection types. Instead of explicitly repeating these operations for each collection type, they are defined once
for Collection(t). Examples for operations which are “inherited” in this way are the size and includes operations
which determine the number of elements in a collection or test for the presence of an element in a collection,
respectively.
A.2.5.2
O PERATIONS
C ONSTRUCTORS
The most obvious way to create a collection value is by explicitly enumerating its element values. We therefore
define a set of generic operations which allow us to construct sets, sequences, and bags from an enumeration of
element values. For example, the set {1, 2, 5} can be described in OCL by the expression Set{1,2,5}, the list
h1, 2, 5i by Sequence{1,2,5}, and the bag {{2, 2, 7}} by Bag{2,2,7}. A shorthand notation for collections
containing integer intervals can be used by specifying lower and upper bounds of the interval. For example, the
expression Sequence{3..6} denotes the sequence h3, 4, 5, 6i. This is only syntactic sugar because the same
collection can be described by explicitly enumerating all values of the interval.
Operations for constructing collection values by enumerating their element values are called constructors. For
types t ∈ TExpr (T̂ ) constructors in ΩTExpr (T̂ ) are defined below. A parameter list t × · · · × t denotes n (n ≥ 0)
parameters of the same type t. We define constructors mkSett , mkSequencet , and mkBagt not only for any type t
but also for any finite number n of parameters.
• mkSett : t × · · · × t → Set(t)
• mkSequencet : t × · · · × t → Sequence(t)
• mkBagt : t × · · · × t → Bag(t)
The semantics of constructors is defined for values v1 , . . . , vn ∈ I(t) by the following functions.
• I(mkSett )(v1 , . . . , vn ) = {v1 , . . . , vn }
• I(mkSequencet )(v1 , . . . , vn ) = hv1 , . . . , vn i
• I(mkBagt )(v1 , . . . , vn ) = {{v1 , . . . , vn }}
A tuple constructor in OCL specifies values and labels for all components, for example, Tuple{number:3,
fruit:’apple’, flag:true}. A constructor for a tuple with component types t1 , . . . , tn ∈ TExpr (T̂ )
(n ≥ 1) is given in abstract syntax by the following operation.
• mkTuple : l1 : t1 × · · · × ln : tn → Tuple(l1 : t1 , . . . , ln : tn )
The semantics of tuple constructors is defined for values vi ∈ I(ti ) with i = 1, . . . , n by the following function.
• I(mkTuple)(l1 : v1 , . . . , ln : vn ) = (v1 , . . . , vn )
Note that constructors having element values as arguments are deliberately defined not to be strict. A collection
value therefore may contain undefined values while still being well-defined.
A-17
S EMANTICS
C OLLECTION
OPERATIONS
The definition of operations of collection types comprises the set of all predefined collection operations. Operations
common to the types Set(t), Sequence(t), and Bag(t) are defined for the supertype Collection(t). Table A.3 shows
the operation schema for these operations. For all t ∈ TExpr (T̂ ), the signatures resulting from instantiating the
schema are included in ΩTExpr (T̂ ) . The right column of the table illustrates the intended set-theoretic interpretation.
For this purpose, C, C1 , C2 are values of type Collection(t), and v is a value of type t.
size :
count :
includes :
excludes :
includesAll :
excludesAll :
isEmpty :
notEmpty :
sum :
Signature
Collection(t) → Integer
Collection(t) × t → Integer
Collection(t) × t → Boolean
Collection(t) × t → Boolean
Collection(t) × Collection(t) → Boolean
Collection(t) × Collection(t) → Boolean
Collection(t) → Boolean
Collection(t) → Boolean
Collection(t) → t
Semantics
|C|
|C ∩ {v}|
v∈C
v∈
/C
C2 ⊆ C1
C2 ∩ C1 = ∅
C=∅
C 6= ∅
P|C|
i=1 ci
Table A.3: Operations for type Collection(t)
The operation schema in Table A.3 can be applied to sets (sequences, bags) by substituting Set(t) (Sequence(t),
Bag(t)) for all occurrences of type Collection(t). A semantics for the operations in Table A.3 can be easily defined
for each of the concrete collection types Set(t), Sequence(t), and Bag(t). The semantics for the operations of
Collection(t) can then be reduced to one of the three cases of the concrete types because every collection type is
either a set, a sequence, or a bag. Consider, for example, the operation count : Set(t) × t → Integer that counts the
number of occurrences of an element v in a set s. The semantics of count is


1 if v ∈ s,
I(count : Set(t) × t → Integer)(s, v) = 0 if v ∈
/ s,


⊥ if s = ⊥.
Note that count is not strict. A set may contain the undefined value so that the result of count is 1 if the undefined
value is passed as the second argument, for example, count({⊥}, ⊥) = 1 and count({1}, ⊥) = 0.
For bags (and very similar for sequences), the meaning of count is
I(count : Bag(t) × t → Integer)({{v1 , . . . , vn }}, v)


0
= I(count)({{v2 , . . . , vn }}, v)


I(count)({{v2 , . . . , vn }}, v) + 1
if n = 0,
if n > 0 and v1 6= v,
if n > 0 and v1 = v.
As explained before, the semantics of count for values of type Collection(t) can now be defined in terms of the
semantics of count for sets, sequences, and bags.
I(count : Collection(t) × t → Integer)(c, v)


I(count : Set(t) × t → Integer)(c, v)



I(count : Sequence(t) × t → Integer)(c, v)
=

I(count : Bag(t) × t → Integer)(c, v)



⊥
if c ∈ I(Set(t)),
if c ∈ I(Sequence(t)),
if c ∈ I(Bag(t)),
otherwise.
A-18
S EMANTICS
S ET
OPERATIONS
Operations on sets include the operations listed in Table A.3. These are inherited from Collection(t). Operations
which are specific to sets are shown in Table A.4 where S, S1 , S2 are values of type Set(t), B is a value of type
Bag(t) and v is a value of type t.
Signature
union : Set(t) × Set(t) → Set(t)
union : Set(t) × Bag(t) → Bag(t)
intersection : Set(t) × Set(t) → Set(t)
intersection : Set(t) × Bag(t) → Set(t)
− : Set(t) × Set(t) → Set(t)
symmetricDifference : Set(t) × Set(t) → Set(t)
including : Set(t) × t → Set(t)
excluding : Set(t) × t → Set(t)
asSequence : Set(t) → Sequence(t)
asBag : Set(t) → Bag(t)
Semantics
S1 ∪ S2
S∪B
S1 ∩ S2
S∩B
S1 − S2
(S1 ∪ S2 ) − (S1 ∩ S2 )
S ∪ {v}
S − {v}
Table A.4: Operations for type Set(t)
Note that the semantics of the operation asSequence is nondeterministic. Any sequence containing only the elements of the source set (in arbitrary order) satisfies the operation specification in OCL.
BAG
OPERATIONS
Operations for bags are shown in Table A.5. The operation asSequence is nondeterministic also for bags.
union :
union :
intersection :
intersection :
including :
excluding :
asSequence :
asSet :
Signature
Bag(t) × Bag(t) → Bag(t)
Bag(t) × Set(t) → Bag(t)
Bag(t) × Bag(t) → Bag(t)
Bag(t) × Set(t) → Set(t)
Bag(t) × t → Bag(t)
Bag(t) × t → Bag(t)
Bag(t) → Sequence(t)
Bag(t) → Set(t)
Semantics
B1 ∪ B2
B∪S
B1 ∩ B2
B∩S
B ∪ {{v}}
B − {{v}}
Table A.5: Operations for type Bag(t)
S EQUENCE
OPERATIONS
Sequence operations are displayed in Table A.6. The intended semantics again is shown in the right column of
the table. S, S1 , S2 are sequences occurring as argument values, v is a value of type t, and i, j are arguments of
type Integer. The length of sequence S is n. The operator ◦ denotes the concatenation of lists, πi (S) projects
the ith element of a sequence S, and πi,j (S) results in a subsequence of S starting with the ith element up to and
including the jth element. The result is ⊥ if an index is out of range. S − hvi produces a sequence equal to S but
with all elements equal to v removed. Note that the operations append and including are also defined identically
in the OCL standard.
A-19
S EMANTICS
union :
append :
prepend :
subSequence :
at :
first :
last :
including :
excluding :
asSet :
asBag :
Signature
Sequence(t) × Sequence(t) → Sequence(t)
Sequence(t) × t → Sequence(t)
Sequence(t) × Integer × Integer → Sequence(t)
Sequence(t) × Integer → t
Sequence(t) → t
Sequence(t) → t
Sequence(t) → Set(t)
Sequence(t) → Bag(t)
Semantics
S1 ◦ S2
S ◦ hei
hei ◦ S
πi,j (S)
πi (S)
π1 (S)
πn (S)
S ◦ hei
S − hei
Table A.6: Operations for type Sequence(t)
F LATTENING
OF COLLECTIONS
Type expressions as introduced in Definition A.24 allow arbitrarily deep nested collection types. We pursue the
following approach for giving a precise meaning to collection flattening. First, we keep nested collection types
because they do not only make the type system more orthogonal, but they are also necessary for describing the
input of the flattening process. Second, we define flattening by means of an explicit function making the effect of
the flattening process clear. There may be a shorthand notation omitting the flatten operation in concrete syntax
which would expand in abstract syntax to an expression with an explicit flattening function.
Flattening in OCL does apply to all collection types. We have to consider all possible combinations first. Table A.7
shows all possibilities for combining Set, Bag, and Sequence into a nested collection type. For each of the different
cases, the collection type resulting from flattening is shown in the right column. Note that the element type t can
be any type. In particular, if t is also a collection type the indicated rules for flattening can be applied recursively
until the element type of the result is a non-collection type.
Nested collection type
Set(Sequence(t))
Set(Set(t))
Set(Bag(t))
Bag(Sequence(t))
Bag(Set(t))
Bag(Bag(t))
Sequence(Sequence(t))
Sequence(Set(t))
Sequence(Bag(t))
Type after flattening
Set(t)
Set(t)
Set(t)
Bag(t)
Bag(t)
Bag(t)
Sequence(t)
Sequence(t)
Sequence(t)
Table A.7: Flattening of nested collections.
A signature schema for a flatten operation that removes one level of nesting can be defined as
flatten : C1 (C2 (t)) → C1 (t)
where C1 and C2 denote any collection type name Set, Sequence, or Bag. The meaning of the flatten operations
can be defined by the following generic iterate expression. The semantics of OCL iterate expressions is defined in
Section A.3.1.2.
A-20
S EMANTICS
<collection-of-type-C1(C2(t))>->iterate(e1 : C2(t);
acc1 : C1(t) = C1{} |
e1->iterate(v : t;
acc2 : C1(t) = acc1 |
acc2->including(v)))
The following example shows how this expression schema is instantiated for a bag of sets of integers, that is,
C1 = Bag, C2 = Set, and t = Integer. The result of flattening the value Bag{Set{3,2},Set{1,2,4}} is
Bag{1,2,2,3,4}.
Bag{Set{3,2},Set{1,2,4}}->iterate(e1 : Set(Integer);
acc1 : Bag(Integer) = Bag{} |
e1->iterate(v : Integer;
acc2 : Bag(Integer) = acc1 |
acc2->including(v)))
It is important to note that flattening sequences of sets and bags (see the last two rows in Table A.7) is potentially
nondeterministic. For these two cases, the flatten operation would have to map each element of the (multi-) set
to a distinct position in the resulting sequence, thus imposing an order on the elements which did not exist in the
first place. Since there are types (e.g. object types) which do not define an order on their domain elements, there
is no obvious mapping for these types. Fortunately, these problematic cases do not occur in standard navigation
expressions. Furthermore, these kinds of collections can be flattened if the criteria for ordering the elements is
explicitly specified.
T UPLE
OPERATIONS
An essential operation for tuple types is the projection of a tuple value onto one of its components. An element of
a tuple with labeled components can be accessed by specifying its label.
• elementli : Tuple(l1 : t1 , . . . , li : ti , . . . , ln : tn ) → ti
• I(elementli : Tuple(l1 : t1 , . . . , li : ti , . . . , ln : tn ) → ti )(v1 , . . . , vi , . . . , vn ) = vi
A.2.6
S PECIAL T YPES
Special types in OCL that do not fit into the categories discussed so far are OclAny, OclState and OclVoid.
• OclAny is the supertype of all other types except for the collection types. The exception has been introduced
in UML 1.3 because it considerably simplifies the type system [CKM+ 99]. A simple set inclusion semantics for subtype relationships as proposed in the next section would not be possible due to cyclic domain
definitions if OclAny were the supertype of Set(OclAny).
• OclState is a type very similar to an enumeration type. It is only used in the operation oclInState for referring
to state names in a state machine. There are no operations defined on this type. OclState is therefore not
treated specially.
• OclVoid is the subtype of all other types. The only value of this type is the undefined value. Notice that there
is no problem with cyclic domain definitions as ⊥ is an instance of every type.
A-21
S EMANTICS
D EFINITION A.26 (S PECIAL T YPES )
The set of special types is TS = {OclAny, OclVoid}.
Let T̂ be the setSof basic,enumeration, and object types T̂ = TB ∪ TE ∪ TC . The domain of OclAny is given as
I(OclAny) =
t∈T̂ I(t) ∪ {⊥}.
The domain of OclVoid is I(OclVoid) = {⊥}.
Operations on OclAny include equality (=) and inequality (<>) which already have been defined for all types
in Section A.2.2. The operations oclIsKindOf, oclIsTypeOf, and oclAsType expect a type as argument. We
define them as part of the OCL expression syntax in the next section. The operation oclIsNew is only allowed in
postconditions and will be discussed in Section A.3.2.
For OclVoid, the constant operation undefined :→ OclVoid results in the undefined value ⊥. The semantics is
given by I(undefined) = ⊥.
A.2.7
T YPE H IERARCHY
The type system of OCL supports inclusion polymorphism [CW85] by introducing the concept of a type hierarchy.
The type hierarchy is used to define the notion of type conformance. Type conformance is a relationship between
two types, expressed by the conformsTo () operation from the abstract syntax metamodel. A valid OCL expression
is an expression in which all the types conform. The consequence of type conformance can be loosely stated as: a
value of a conforming type B may be used wherever a value of type A is required.
The type hierarchy reflects the subtype/supertype relationship between types. The following relationships are
defined in OCL.
1. Integer is a subtype of Real.
2. All types, except for the collection and tuple types, are subtypes of OclAny.
3. Set(t), Sequence(t), and Bag(t) are subtypes of Collection(t).
4. OclVoid is subtype of all other types.
5. The hierarchy of types introduced by UML model elements mirrors the generalization hierarchy in the UML
model.
Type conformance is a relation which is identical to the subtype relation introduced by the type hierarchy. The
relation is reflexive and transitive.
D EFINITION A.27 (T YPE HIERARCHY )
Let T be a set of types and TC a set of object types with TC ⊂ T . The relation ≤ is a partial order on T and is
called the type hierarchy over T . The type hierarchy is defined for all t, t0 , t00 ∈ T and all tc , t0c ∈ TC , n, m ∈ N as
follows.
i. ≤ is (a) reflexive, (b) transitive, and (c) antisymmetric:
(a) t ≤ t
(b) t00 ≤ t0 ∧ t0 ≤ t =⇒ t00 ≤ t
(c) t0 ≤ t ∧ t ≤ t0 =⇒ t = t0 .
ii. Integer ≤ Real.
A-22
S EMANTICS
iii. t ≤ OclAny for all t ∈ (TB ∪ TE ∪ TC ).
iv. OclVoid ≤ t.
v. Set(t) ≤ Collection(t),
Sequence(t) ≤ Collection(t), and
Bag(t) ≤ Collection(t).
vi. If t0 ≤ t then Set(t0 ) ≤ Set(t), Sequence(t0 ) ≤ Sequence(t), Bag(t0 ) ≤ Bag(t), and
Collection(t0 ) ≤ Collection(t).
vii. If t0i ≤ ti for i = 1, . . . , n and n ≤ m then
Tuple(l1 : t01 , . . . , ln : t0n , . . . , lm : t0m ) ≤ Tuple(l1 : t1 , . . . , ln : tn ).
viii. If classOf(t0c ) ≺ classOf(tc ) then t0c ≤ tc .
If a type t0 is a subtype of another type t (i.e. t0 ≤ t), we say that t0 conforms to t. Type conformance is associated
with the principle of substitutability. A value of type t0 may be used wherever a value of type t is expected. This
rule is defined more formally in Section A.3.1 which defines the syntax and semantics of expressions.
The principle of substitutability and the interpretation of types as sets suggest that the type hierarchy should be
defined as a subset relation on the type domains. Hence, for a type t0 being a subtype of t, we postulate that the
interpretation of t0 is a subset of the interpretation of t. It follows that every operation ω accepting values of type t
has the same semantics for values of type t0 , since I(ω) is already well-defined for values in I(t0 ):
If t0 ≤ t then I(t0 ) ⊆ I(t) for all types t0 , t ∈ T .
A.2.8
DATA S IGNATURE
We now have available all elements necessary to define the final data signature for OCL expressions. The signature
provides the basic set of syntactic elements for building expressions. It defines the syntax and semantics of types,
the type hierarchy, and the set of operations defined on types.
D EFINITION A.28 (DATA SIGNATURE )
Let T̂ be the set of non-collection types: T̂ = TB ∪ TE ∪ TC ∪ TS . The syntax of a data signature over an object
model M is a structure ΣM = (TM , ≤, ΩM ) where
i. TM = TExpr (T̂ ),
ii. ≤ is a type hierarchy over TM ,
iii. ΩM = ΩTExpr (T̂ ) ∪ ΩB ∪ ΩE ∪ ΩC ∪ ΩS .
The semantics of ΣM is a structure I(ΣM ) = (I(TM ), I(≤), I(ΩM )) where
i. I(TM ) assigns each t ∈ TM an interpretation I(t).
ii. I(≤) implies for all types t0 , t ∈ TM that I(t0 ) ⊆ I(t) if t0 ≤ t.
iii. I(ΩM ) assigns each operation ω : t1 × · · · × tn → t ∈ ΩM a total function
I(ω) : I(t1 ) × · · · × I(tn ) → I(t).
A-23
S EMANTICS
A.3
OCL E XPRESSIONS AND C ONSTRAINTS
The core of OCL is given by an expression language. Expressions can be used in various contexts, for example,
to define constraints such as class invariants and pre-/postconditions on operations. In this section, we formally
define the syntax and semantics of OCL expressions, and give precise meaning to notions like context, invariant,
and pre-/postconditions.
Section A.3.1 defines the abstract syntax and semantics of OCL expressions and shows how other OCL constructs
can be derived from this language core. The context of expressions and other important concepts such as invariants,
queries, and shorthand notations are discussed. Section A.3.2 defines the meaning of operation specifications with
pre- and postconditions.
A.3.1
E XPRESSIONS
In this section, we define the syntax and semantics of expressions. The definition of expressions is based upon
the data signature we developed in the previous section. A data signature ΣM = (TM , ≤, ΩM ) provides a set of
types TM , a relation ≤ on types reflecting the type hierarchy, and a set of operations ΩM . The signature contains
the initial set of syntactic elements upon which we build the expression syntax.
A.3.1.1
S YNTAX
OF
E XPRESSIONS
We define the syntax of expressions inductively so that more complex expressions are recursively built from simple
structures. For each expression the set of free occurrences of variables is also defined. Also, each section in the
definition corresponds to a subclass of OCLExpression in the abstract syntax. The mapping is indicated.
D EFINITION A.29 (S YNTAX OF EXPRESSIONS )
Let ΣM = (TM , ≤, ΩM ) be a data signature over an object model M. Let Var = {Vart }t∈TM be a family of
variable sets where each variable set is indexed by a type t. The syntax of expressions over the signature ΣM is
given by a set Expr = {Exprt }t∈TM and a function free : Expr → F(Var) that are defined as follows.
i. If v ∈ Vart then v ∈ Exprt and free(v) := {v}. This maps into the VariableExp class in the abstract
syntax.
ii. If v ∈ Vart1 , e1 ∈ Exprt1 , e2 ∈ Exprt2 then let v = e1 in e2 ∈ Exprt2 and
free(let v = e1 in e2 ) := free(e2 ) − {v}. This maps into LetExpression in the abstract syntax. v = e1 is
the VariableDeclaration referred through the variable association; e2 is the OclExpression referred
through association end in. e1 is the OclExpression referred from the VariableDeclaration through the
initExpression association.
iii.
(a) If t ∈ TM and ω :→ t ∈ ΩM then ω ∈ Exprt and undefined ∈ ExprOclVoid and free(ω) := ∅ and
free(undefined) := ∅. This maps into the ConstantExp class and its subclasses from the abstract
syntax.
(b) If ω : t1 × · · · × tn → t ∈ ΩM and ei ∈ Exprti for all i = 1, . . . , n then ω(e1 , . . . , en ) ∈ Exprt and
free(ω(e1 , . . . , en )) := free(e1 ) ∪ · · · ∪ free(en ). This maps into ModelPropertyCallExp and its
subclasses, with e1 representing the source and e2 to en the arguments.
A-24
S EMANTICS
iv. If e1 ∈ ExprBoolean and e2 , e3 ∈ Exprt then if e1 then e2 else e3 endif ∈ Exprt and
free(if e1 then e2 else e3 endif) := free(e1 ) ∪ free(e2 ) ∪ free(e3 ). This corresponds to the IfExpression in
the abstract syntax. e1 is the OclExpression referred through condition, e2 corresponds to the
thenExpression association, and e3 maps into the OclExpression elseExpression.
v. If e ∈ Exprt and t0 ≤ t or t ≤ t0 then (e asType t0 ) ∈ Exprt0 , (e isTypeOf t0 ) ∈ ExprBoolean ,
(e isKindOf t0 ) ∈ ExprBoolean and free((e asType t0 )) := free(e), free((e isTypeOf t0 )) := free(e),
free((e isKindOf t0 )) := free(e). This maps into some special instances of
OclOperationWithTypeArgument.
vi. If e1 ∈ ExprCollection(t1 ) , v1 ∈ Vart1 , v2 ∈ Vart2 , and e2 , e3 ∈ Exprt2 then e1 → iterate(v1 ; v2 = e2 | e3 )
∈ Exprt2 and free(e1 → iterate(v1 ; v2 = e2 | e3 )) := (free(e1 ) ∪ free(e2 ) ∪ free(e3 )) − {v1 , v2 }. This is a
representation of the IterateExp. e1 is the source, v2 = e2 is the VariableDeclaration which is referred to
through the result association in the abstract syntax. v1 corresponds to the iterator VariableDeclaration.
Finally, e3 is the OclExpression body. Instances of IteratorExp are defined in the OCL Standard Library.
An expression of type t0 is also an expression of a more general type t. For all t0 ≤ t: if e ∈ Exprt0 then e ∈ Exprt .
A variable expression (i) refers to the value of a variable. Variables (including the special variable self) may
be introduced by the context of an expression, as part of an iterate expression, and by a let expression. Let
expressions (ii) do not add to the expressiveness of OCL but help to avoid repetitions of common sub-expressions.
Constant expressions (iiia) refer to a value from the domain of a type. Operation expressions (iiib) apply an
operation from ΩM . The set of operations includes:
• predefined data operations: +, -, *, <, >, size, max
• attribute operations: self.age, e.salary
• side effect-free operations defined by a class:
b.rentalsForDay(...)
• navigation by role names: self.employee
As demonstrated by the examples, an operation expression may also be written in OCL path syntax as
e1 .ω(e2 , . . . , en ). This notational style is common in many object-oriented languages. It emphasizes the role
of the first argument as the “receiver” of a “message”. If e1 denotes a collection value, an arrow symbol is used in
OCL instead of the period: e1 → ω(e2 , . . . , en ). Collections may be bags, sets, or lists.
An if-expression (iv) provides an alternative selection of two expressions depending on the result of a condition
given by a boolean expression.
An asType expression (v) can be used in cases where static type information is insufficient. It corresponds to
the oclAsType operation in OCL and can be understood as a cast of a source expression to an equivalent expression of a (usually) more specific target type. The target type must be related to the source type, that is, one
must be a subtype of the other. The isTypeOf and isKindOf expressions correspond to the oclIsTypeOf and
oclIsKindOf operations, respectively. An expression (e isTypeOf t0 ) can be used to test whether the type of the
value resulting from the expression e has the type t0 given as argument. An isKindOf expression (e isKindOf t0 ) is
not as strict in that it is sufficient for the expression to become true if t0 is a supertype of the type of the value of e.
Note that in previous OCL versions these type casts and tests were defined as operations with parameters of type
OclType. Here, we technically define them as first class expressions which has the benefit that we do not need the
metatype OclType. Thus the type system is kept simple while preserving compatibility with standard OCL syntax.
A-25
S EMANTICS
An iterate expression (vi) is a general loop construct which evaluates an argument expression e3 repeatedly for
all elements of a collection which is given by a source expression e1 . Each element of the collection is bound in
turn to the variable v1 for each evaluation of the argument expression. The argument expression e3 may contain
the variable v1 to refer to the current element of the collection. The result variable v2 is initialized with the
expression e2 . After each evaluation of the argument expression e3 , the result is bound to the variable v2 . The final
value of v2 is the result of the whole iterate expression.
The iterate construct is probably the most important kind of expression in OCL. Many other OCL constructs (such
as select, reject, collect, exists, forAll, and isUnique) can be equivalently defined in terms of
an iterate expression (see Section A.3.1.3).
Following the principle of substitutability, the syntax of expressions is defined such that wherever an expression
e ∈ Exprt is expected as part of another expression, an expression with a more special type t0 , (t0 ≤ t) may be
used. In particular, operation arguments and variable assignments in let and iterate expressions may be given by
expressions of more special types.
A.3.1.2
S EMANTICS
OF
E XPRESSIONS
The semantics of expressions is made precise in the following definition. A context for evaluation is given by an
environment τ = (σ, β) consisting of a system state σ and a variable assignment β : Vart → I(t). A system
state σ provides access to the set of currently existing objects, their attribute values, and association links between
objects. A variable assignment β maps variable names to values.
D EFINITION A.30 (S EMANTICS OF EXPRESSIONS )
Let Env be the set of environments τ = (σ, β). The semantics of an expression e ∈ Exprt is a function I[[ e ]] :
Env → I(t) that is defined as follows.
i. I[[ v ]](τ ) = β(v).
ii. I[[ let v = e1 in e2 ]](τ ) = I[[ e2 ]](σ, β{v/I[[ e1 ]](τ )}).
iii. I[[ undefined ]](τ ) = ⊥ and I[[ ω ]](τ ) = I(ω)
iv. I[[ ω(e1 , . . . , en ) ]](τ ) = I(ω)(τ )(I[[ e1 ]](τ ), . . . , I[[ en ]](τ )).


I[[ e2 ]](τ ) if I[[ e1 ]](τ ) = true,
v. I[[ if e1 then e2 else e3 endif ]](τ ) = I[[ e3 ]](τ ) if I[[ e1 ]](τ ) = false,


⊥
otherwise.
(
I[[ e ]](τ ) if I[[ e ]](τ ) ∈ I(t0 ),
0
vi. I[[ (e asType t ) ]](τ ) =
⊥
otherwise.
(
S
true if I[[ e ]](τ ) ∈ I(t0 ) − t00 <t0 I(t00 ),
0
I[[ (e isTypeOf t ) ]](τ ) =
false otherwise.
(
true if I[[ e ]](τ ) ∈ I(t0 ),
I[[ (e isKindOf t0 ) ]](τ ) =
false otherwise.
vii. I[[ e1 → iterate(v1 ; v2 = e2 | e3 ) ]](τ ) = I[[ e1 → iterate0 (v1 | e3 ) ]](τ 0 ) where τ 0 = (σ, β 0 ) and τ 00 = (σ, β 00 )
are environments with modified variable assignments
β 0 := β{v2 /I[[ e2 ]](τ )}
β 00 := β 0 {v2 /I[[ e3 ]](σ, β 0 {v1 /x1 })}
and iterate0 is defined as:
A-26
S EMANTICS
(a) If e1 ∈ ExprSequence(t1 ) then

0

I[[ v2 ]](τ )


 if I[[ e ]](τ 0 ) = hi,
1
I[[ e1 → iterate0 (v1 | e3 ) ]](τ 0 ) =
0
00

I[[
mkSequence

t1 (x2 , . . . , xn ) → iterate (v1 | e3 ) ]](τ )


 if I[[ e ]](τ 0 ) = hx , . . . , x i.
1
1
n
(b) If e1 ∈ ExprSet(t1 ) then


I[[ v2 ]](τ 0 )



 if I[[ e ]](τ 0 ) = ∅,
1
I[[ e1 → iterate0 (v1 | e3 ) ]](τ 0 ) =
0
00

I[[
mkSet
t1 (x2 , . . . , xn ) → iterate (v1 | e3 ) ]](τ )



 if I[[ e ]](τ 0 ) = {x , . . . , x }.
1
1
n
(c) If e1 ∈ ExprBag(t1 ) then


I[[ v2 ]](τ 0 )



 if I[[ e ]](τ 0 ) = ∅,
1
I[[ e1 → iterate0 (v1 | e3 ) ]](τ 0 ) =
I[[ mkBagt (x2 , . . . , xn ) → iterate0 (v1 | e3 ) ]](τ 00 )

1


 if I[[ e ]](τ 0 ) = {{x , . . . , x }}.
1
1
n
The semantics of a variable expression (i) is the value assigned to the variable. A let expression (ii) results in the
value of the sub-expression e2 . Free occurrences of the variable v in e2 are bound to the value of the expression e1 .
An operation expression (iv) is interpreted by the function associated with the operation. Each argument expression
is evaluated separately. The state σ is passed to operations whose interpretation depends on the system state. These
include, for example, attribute and navigation operations as defined in Section A.2.4.
The computation of side effect-free operations can often be described with OCL expressions. We can extend the
definition to allow object operations whose effects are defined in terms of OCL expressions. The semantics of a
side effect-free operation can then be given by the semantics of the OCL expression associated with the operation.
Recall that object operations in O Pc are declared in a model specification. Let oclexp : O Pc → Expr be a
partial function mapping object operations to OCL expressions. We define the semantics of an operation with an
associated OCL expression as
I[[ ω(p1 : e1 , . . . , pn : en ) ]](τ ) = I[[ oclexp(ω) ]](τ 0 )
where p1 , . . . , pn are parameter names, and τ 0 = (σ, β 0 ) denotes an environment with a modified variable assignment defined as
β 0 := β{p1 /I[[ e1 ]](τ ), . . . , pn /I[[ en ]](τ )} .
Argument expressions are evaluated and assigned to parameters that bind free occurrences of p1 , . . . , pn in the expression oclexp(ω). For a well-defined semantics, we need to make sure that there is no infinite recursion resulting
from an expansion of the operation call. A strict solution that can be statically checked is to forbid any occurrences
of ω in oclexp(ω). However, allowing recursive operation calls considerably adds to the expressiveness of OCL.
We therefore allow recursive invocations as long as the recursion is finite. Unfortunately, this property is generally
undecidable.
The result of an if-expression (v) is given by the then-part if the condition is true. If the condition is false, the elsepart is the result of the expression. An undefined condition makes the whole expression undefined. Note that when
an expression in one of the alternative branches is undefined, the whole expression may still have a well-defined
result. For example, the result of the following expression is 1.
A-27
S EMANTICS
if true then 1 else 1 div 0 endif
The result of a cast expression (vi) using asType is the value of the expression, if the value lies within the domain
of the specified target type, otherwise it is undefined. A type test expression with isTypeOf is true if the expression
value lies exactly within the domain of the specified target type without considering subtypes. An isKindOf type
test expression is true if the expression value lies within the domain of the specified target type or one of its
subtypes. Note that these type cast and test expressions also work with undefined values since every value –
including an undefined one – has a well-defined type.
An iterate expression (vii) loops over the elements of a collection and allows the application of a function to each
collection element. The function results are successively combined into a value that serves as the result of the
whole iterate expression. This kind of evaluation is also known in functional style programming languages as fold
operation (see, e.g., [Tho99]).
In Definition A.30, the semantics of iterate expressions is given by a recursive evaluation scheme. Information is
passed between different levels of recursion by modifying the variable assignment β appropriately in each step.
The interpretation of iterate starts with the initialization of the accumulator variable. The recursive evaluation
following thereafter uses a simplified version of iterate, namely an expression iterate0 where the initialization of the
accumulator variable is left out, since this sub-expression needs to be evaluated only once. If the source collection
is not empty, (1) an element from the collection is bound to the iteration variable, (2) the argument expression is
evaluated, and (3) the result is bound to the accumulator variable. These steps are all part of the definition of the
variable assignment β 00 . The recursion terminates when there are no more elements in the collection to iterate over.
The constructor operations mkSequencet , mkBagt , and mkSett (see page 17) are in ΩM and provide the abstract
syntax for collection literals like Set{1,2} in concrete OCL syntax.
The result of an iterate expression applied to a set or bag is deterministic only if the inner expression is both
commutative and associative.
A.3.1.3
D ERIVED E XPRESSIONS BASED
ON ITERATE
A number of important OCL constructs such as exists, forAll, select, reject, collect, and
isUnique are defined in terms of iterate expressions. The following schema shows how these expressions can
be translated to equivalent iterate expressions. A similar translation can be found in [Cla99].
I[[ e1 → exists(v1 | e3 ) ]](τ ) =
I[[ e1 → iterate(v1; v2 = false | v2 or e3 ) ]](τ )
I[[ e1 → forAll(v1 | e3 ) ]](τ ) =
I[[ e1 → iterate(v1; v2 = true | v2 and e3 ) ]](τ )
I[[ e1 → select(v1 | e3 ) ]](τ ) =
I[[ e1 → iterate(v1; v2 = e1 |
if e3 then v2 else v2 → excluding(v1 ) endif) ]](τ )
I[[ e1 → reject(v1 | e3 ) ]](τ ) =
I[[ e1 → iterate(v1; v2 = e1 |
if e3 then v2 → excluding(v1 ) else v2 endif) ]](τ )
I[[ e1 → collect(v1 | e3 ) ]](τ ) =
I[[ e1 → iterate(v1; v2 = mkBagtype-of-e3 () | v2 → including(e3 )) ]](τ )
I[[ e1 → isUnique(v1 | e3 ) ]](τ ) =
A-28
S EMANTICS
I[[ e1 → iterate(v1; v2 = true | v2 and e1 → count(v1 ) = 1) ]](τ )
A.3.1.4
E XPRESSION C ONTEXT
An OCL expression is always written in some syntactical context. Since the primary purpose of OCL is the
specification of constraints on a UML model, it is obvious that the model itself provides the most general kind
of context. In our approach, the signature ΣM contains types (e.g., object types) and operations (e.g., attribute
operations) that are “imported” from a model, thus providing a context for building expressions that depend on the
elements of a specific model.
On a much smaller scale, there is also a notion of context in OCL that simply introduces variable declarations.
This notion is closely related to the syntax for constraints written in OCL. A context clause declares variables in
invariants, and parameters in pre- and postconditions.
A context of an invariant is a declaration of variables. The variable declaration may be implicit or explicit. In the
implicit form, the context is written as
context C inv:
<expression>
In this case, the <expression> may use the variable self of type C as a free variable. In the explicit form,
the context is written as
context v1 : C1 , . . . , vn : Cn inv:
<expression>
The <expression> may use the variables v1 , . . . , vn of types C1 , . . . , Cn as free variables.
A context of a pre-/postcondition is a declaration of variables. In this case, the context is written as
context C :: op(p1 : T1 , . . . , pn : Tn ) : T
pre: P
post: Q
This means that the variable self (of type C) and the parameters p1 , . . . , pn may be used as free variables in the
precondition P and the postcondition Q. Additionally, the postcondition may use result (of type T) as a free
variable. The details are explained in Section A.3.2.
A.3.1.5
I NVARIANTS
An invariant is an expression with boolean result type and a set of (explicitly or implicitly declared) free variables
v1 : C1 , . . . , vn : Cn where C1 , . . . , Cn are classifier types. An invariant
context v1 : C1 , . . . , vn : Cn inv:
<expression>
is equivalent to the following expression without free variables that must be valid in all system states.
A-29
S EMANTICS
C1 .allInstances->forAll(v1 : C1 |
...
Cn .allInstances->forAll(vn : Cn |
<expression>
)
...
)
A system state is called valid with respect to an invariant if the invariant evaluates to true. Invariants with undefined
result invalidate a system state.
A.3.2
P RE - AND P OSTCONDITIONS
The definition of expressions in the previous section is sufficient for invariants and queries where we have to
consider only single system states. For pre- and postconditions, there are additional language constructs in OCL
which enable references to the system state before the execution of an operation and to the system state that results
from the operation execution. The general syntax of an operation specification with pre- and postconditions is
defined as
context C :: op(p1 : T1 , . . . , pn : Tn )
pre: P
post: Q
First, the context is determined by giving the signature of the operation for which pre- and postconditions are
to be specified. The operation op which is defined as part of the classifier C has a set of typed parameters
PARAMSop = {p1 , . . . , pn }. The UML model providing the definition of an operation signature also specifies the
direction kind of each parameter. We use a function kind : PARAMSop → {in, out, inout, return} to map each
parameter to one of these kinds. Although UML makes no restriction on the number of return parameters, there is
usually only at most one return parameter considered in OCL which is referred to by the keyword result in a
postcondition. In this case, the signature is also written as C :: op(p1 : T1 , . . . , pn−1 : Tn−1 ) : T with T being the
type of the result parameter.
The precondition of the operation is given by an expression P , and the postcondition is specified by an expression Q. P and Q must have a boolean result type. If the precondition holds, the contract of the operation guarantees
that the postcondition is satisfied after completion of op. Pre- and postconditions form a pair. A condition defaults
to true if it is not explicitly specified.
A.3.2.1
E XAMPLE
Before we give a formal definition of operation specifications with pre- and postconditions, we demonstrate the
fundamental concepts by means of an example. Figure A.1 shows a class diagram with two classes A and B that are
related to each other by an association R. Class A has an operation op() but no attributes. Class B has an attribute c
and no operations. The implicit role names a and b at the link ends allow navigation in OCL expressions from a B
object to the associated A object and vice versa.
Figure A.2 shows an example for two consecutive states of a system corresponding to the given class model. The
object diagrams show instances of classes A and B and links of the association R. The left object diagram shows
the state before the execution of an operation, whereas the right diagram shows the state after the operation has
been executed. The effect of the operation can be described by the following changes in the post-state: (1) the
A-30
S EMANTICS
A
R
*
op()
*
B
c : Integer
Figure A.1: Example class diagram
R
R
a:A
b1 : B
a:A
c=1
(a) Pre-state with objects a and b1 .
b2 : B
c=0
b1 : B
c=2
(b) Post-state.
Object b2 did not exist in
the pre-state.
Figure A.2: Object diagrams showing a pre- and a post-state
value of the attribute c in object b1 has been incremented by one, (2) a new object b2 has been created, (3) the link
between a and b1 has been removed, and (4) a new link between a and b2 has been established.
For the following discussion, consider the OCL expression a.b.c where a is a variable denoting the object a.
The expression navigates to the associated object of class B and results in the value of the attribute c. Therefore,
the expression evaluates to 1 in the pre-state shown in Figure A.2(a). As an example of how the OCL modifier
@pre may be used in a postcondition to refer to properties of the previous state, we now look at some variations of
the expression a.b.c that may appear as part of a postcondition. For each case, the result is given and explained.
• a.b.c = 0
Because the expression is completely evaluated in the post-state, the navigation from a leads to the b2 object.
The value of the attribute c of b2 is 0 in Figure A.2(b).
• a.b@pre.c = 2
This expression refers to both the pre- and the post-state. The previous value of a.b is a reference to
object b1 . However, since the @pre modifier only applies to the expression a.b, the following reference to
the attribute c is evaluated in the post-state of b1 , even though b1 is not connected anymore to a. Therefore,
the result is 2.
• a.b@pre.c@pre = 1
In this case, the value of the attribute c of object b1 is taken from the pre-state. This expression is semantically
equivalent to the expression a.b.c in a precondition.
• a.b.c@pre = ⊥
The expression a.b evaluated in the post-state yields a reference to object b2 which is now connected to a.
Since b2 has just been created by the operation, there is no previous state of b2 . Hence, a reference to the
previous value of attribute c is undefined.
Note that the @pre modifier may only be applied to operations not to arbitrary expressions. An expression such
as (a.b)@pre is syntactically illegal.
OCL provides the standard operation oclIsNew for checking whether an object has been created during the
execution of an operation. This operation may only be used in postconditions. For our example, the following
conditions indicate that the object b2 has just been created in the post-state and b1 already existed in the pre-state.
A-31
S EMANTICS
• a.b.oclIsNew = true
• a.b@pre.oclIsNew = false
A.3.2.2
S YNTAX
AND
S EMANTICS
OF
P OSTCONDITIONS
All common OCL expressions can be used in a precondition P . Syntax and semantics of preconditions are defined
exactly like those for plain OCL expressions in Section A.3.1. Also, all common OCL expressions can be used in
a postcondition Q. Additionally, the @pre construct, the special variable result, and the operation oclIsNew
may appear in a postcondition. In the following, we extend Definition A.29 for the syntax of OCL expressions to
provide these additional features.
D EFINITION A.31 (S YNTAX OF EXPRESSIONS IN POSTCONDITIONS )
Let op be an operation with a set of parameters PARAMSop . The set of parameters includes at most one parameter
of kind “return”. The basic set of expressions in postconditions is defined by repeating Definition A.29 while
substituting all occurrences of Exprt with Post-Exprt . Furthermore, we define that
• Each non-return parameter p ∈ PARAMSop with a declared type t is available as variable: p ∈ Vart .
• If PARAMSop contains a parameter of kind “return” and type t then result is a variable: result ∈ Vart .
• The operation oclIsNew : c → Boolean is in ΩM for all object types c ∈ TM .
The syntax of expressions in postconditions is extended by the following rule.
vii. If ω : t1 × · · · × tn → t ∈ ΩM and ei ∈ Post-Exprt0 for all i = 1, . . . , n then
ω@pre (e1 , . . . , en ) ∈ Post-Exprt .
All general OCL expressions may be used in a postcondition. Moreover, the basic rules for recursively constructing
expressions do also apply. Operation parameters are added to the set of variables. For operations with a return
type, the variable result refers to the operation result. The set of operations is extended by oclIsNew which is
defined for all object types. Operations ω@pre are added for allowing references to the previous state (vii). The rule
says that the @pre modifier may be applied to all operations, although, in general, not all operations do actually
depend on a system state (for example, operations on data types). The result of these operations will be the same
in all states. Operations which do depend on a system state are, e.g., attribute access and navigation operations.
For a definition of the semantics of postconditions, we will refer to environments describing the previous state
and the state resulting from executing the operation. An environment τ = (σ, β) is a pair consisting of a system
state σ and a variable assignment β (see Section A.3.1.2). The necessity of including variable assignments into
environments will be discussed shortly. We call an environment τpre = (σpre , βpre ) describing a system state and
variable assignments before the execution of an operation a pre-environment. Likewise, an environment τpost =
(σpost , βpost ) after the completion of an operation is called a post-environment.
D EFINITION A.32 (S EMANTICS OF POSTCONDITION EXPRESSIONS )
Let Env be the set of environments. The semantics of an expression e ∈ Post-Exprt is a function I[[ e ]] :
Env × Env → I(t). The semantics of the basic set of expressions in postconditions is defined by repeating
Definition A.30 while substituting all occurrences of Exprt with Post-Exprt . References to I[[ e ]](τ ) are replaced
by I[[ e ]](τpre , τpost ) to include the pre-environment. Occurrences of τ are changed to τpost which is the default
environment in a postcondition.
A-32
S EMANTICS
• For all p ∈ PARAMSop : I[[ p ]](τpre , τpost ) = βpost (p).
– Input parameters may not be modified by an operation:
kind(p) = in implies βpre (p) = βpost (p).
– Output parameters are undefined on entry:
kind(p) = out implies βpre (p) = ⊥.
• I[[ result ]](τpre , τpost ) = βpost (result).
(
/ σpre (c) and c ∈ σpost (c),
true if c ∈
• I[[ oclIsNew ]](τpre , τpost )(c) =
false otherwise.
vii. I[[ ω@pre (e1 , . . . , en ) ]](τpre , τpost ) = I(ω)(τpre )(I[[ e1 ]](τpre , τpost ), . . . , I[[ en ]](τpre , τpost ))
Standard expressions are evaluated as defined in Definition A.30 with the post-environment determining the context
of evaluation. Input parameters do not change during the execution of the operation. Therefore, their values are
equal in the pre- and post-environment. The value of the result variable is determined by the variable assignment
of the post-environment. The oclIsNew operation yields true if an object did not exist in the previous system
state. Operations referring to the previous state are evaluated in context of the pre-environment (vii). Note that
the operation arguments may still be evaluated in the post-environment. Therefore, in a nested expression, the
environment only applies to the current operation, whereas deeper nested operations may evaluate in a different
environment.
With these preparations, the semantics of an operation specification with pre- and postconditions can be precisely
defined as follows. We say that a precondition P satisfies a pre-environment τpre – written as τpre |= P – if the
expression P evaluates to true according to Definition A.30. Similarly, a postcondition Q satisfies a pair of preand post-environments, if the expression Q evaluates to true according to Definition A.32:
τpre |= P
iff
I[[ P ]](τpre ) = true
(τpre , τpost ) |= Q iff I[[ Q ]](τpre , τpost ) = true
D EFINITION A.33 (S EMANTICS OF OPERATION SPECIFICATIONS )
The semantics of an operation specification is a set R ⊆ Env × Env defined as
[[ context C :: op(p1 : T1 , . . . , pn : Tn )
pre: P
post: Q ]] = R
where R is the set of all pre- and post-environment pairs such that the pre-environment τpre satisfies the precondition P and the pair of both environments satisfies the postcondition Q:
R = {(τpre , τpost ) | τpre |= P ∧ (τpre , τpost ) |= Q}
The satisfaction relation for Q is defined in terms of both environments since the postcondition may contain
references to the previous state. The set R defines all legal transitions between two states corresponding to the
effect of an operation. It therefore provides a framework for a correct implementation.
A-33
S EMANTICS
D EFINITION A.34 (S ATISFACTION OF OPERATION SPECIFICATIONS )
An operation specification with pre- and postconditions is satisfied by a program S in the sense of total correctness
if the computation of S is a total function fS : dom(R) → im(R) and graph(fS ) ⊆ R.
In other words, the program S accepts each environment satisfying the precondition as input and produces an
environment that satisfies the postcondition. The definition of R allows us to make some statements about the
specification. In general, a reasonable specification implies a non-empty set R allowing one or more different implementations of the operation. If R = ∅, then there is obviously no implementation possible. We distinguish two
cases: (1) no environment satisfying the precondition exists, or (2) there are environments making the precondition
true, but no environments do satisfy the postcondition. Both cases indicate that the specification is inconsistent
with the model. Either the constraint or the model providing the context should be changed. A more restrictive
definition might even prohibit the second case.
A-34
S EMANTICS
B IBLIOGRAPHY
[AFGP96]
A. Artale, E. Franconi, N. Guarino, and L. Pazzi. Part-whole relations in object-centered systems:
An overview. Data & Knowledge Engineering, 20(3):347–383, November 1996.
[AHV95]
S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.
[BHS99]
F. Barbier and B. Henderson-Sellers. Object metamodelling of the whole-part relationship. In
C. Mingins, editor, Proceedings of TOOLS Pacific 1999. IEEE Computer Society, 1999.
[BHSOG01] F. Barbier, B. Henderson-Sellers, A. L. Opdahl, and M. Gogolla. The whole-part relationship in the
Unified Modeling Language: A new approach. In K. Siau and T. Halpin, editors, Unified Modeling
Language: Systems Analysis, Design and Development Issues, chapter 12, pages 185–209. Idea
Publishing Group, 2001.
[CKM+ 99] S. Cook, A. Kleppe, R. Mitchell, B. Rumpe, J. Warmer, and A. Wills. The Amsterdam manifesto on
OCL. Technical Report TUM-I9925, Technische Universität München, December 1999.
[Cla99]
T. Clark. Type checking UML static diagrams. In R. France and B. Rumpe, editors, UML’99 - The
Unified Modeling Language. Beyond the Standard. Second International Conference, Fort Collins,
CO, USA, October 28-30. 1999, Proceedings, volume 1723 of LNCS, pages 503–517. Springer,
1999.
[CW85]
L. Cardelli and P. Wegner. On understanding types, data abstraction and polymorphism. ACM
Computing Surveys, 17(4):471–522, December 1985.
[Dat90]
C. J. Date. An Introduction to Database Systems – Vol. I. Addison-Wesley, Readings (MA), 1990.
[EN94]
R. Elmasri and S. B. Navathe. Fundamentals of Database Systems. The Benjamin/Cummings Publishing Company, Inc., 2 edition, 1994.
[Gog94]
M. Gogolla. An Extended Entity-Relationship Model – Fundamentals and Pragmatics, volume 767
of LNCS. Springer, Berlin, 1994.
[GR99]
M. Gogolla and M. Richters. Transformation rules for UML class diagrams. In J. Bézivin and P.-A.
Muller, editors, The Unified Modeling Language, UML’98 - Beyond the Notation. First International
Workshop, Mulhouse, France, June 1998, Selected Papers, volume 1618 of LNCS, pages 92–106.
Springer, 1999.
[Her95]
R. Herzig. Zur Spezifikation von Objektgesellschaften mit TROLL light. VDI-Verlag, Düsseldorf,
Reihe 10 der Fortschritt-Berichte, Nr. 336, 1995. (Dissertation, Naturwissenschaftliche Fakultät,
Technische Universität Braunschweig, 1994).
[HSB99]
B. Henderson-Sellers and F. Barbier. Black and white diamonds. In R. France and B. Rumpe, editors,
UML’99 - The Unified Modeling Language. Beyond the Standard. Second International Conference,
Fort Collins, CO, USA, October 28-30. 1999, Proceedings, volume 1723 of LNCS, pages 550–565.
Springer, 1999.
[Mot96]
R. Motschnig-Pitrik. Analyzing the notions of attribute, aggregate, part and member in data/
knowledge modeling. The Journal of Systems and Software, 33(2):113–122, May 1996.
[Pri97]
S. Pribbenow. What’s a part? On formalizing part-whole relations. In Foundations of Computer
Science: Potential – Theory – Cognition, volume 1337 of LNCS, pages 399–406. Springer, 1997.
A-35
S EMANTICS
[Ric02]
M. Richters. A Precise Approach to Validating UML Models and OCL Constraints. Ph.D. thesis,
Universität Bremen, Logos Verlag, Berlin, BISS Monographs, No. 14, 2002.
[Tho99]
S. Thompson. Haskell: The Craft of Functional Programming. Addison-Wesley, 2nd edition, 1999.
A-36
Appendix B - Interchange Format
B.1
This appendix is intentially left blank.
This section contains the interchange format for OCL. This XMI DTD should be generated from the metamodel.
Note – This needs to be done when the final submission is finished.
Note – Note that even the concrete syntax could be used as a simple interchange format, because it only consists of standard
text strings. However. accepting tools would need to (re)parse the concrete syntax. The benefit will be that tools that do not
support OCL (it is a optional compliance point within UML) can still create and interchange OCL as text.
B-1
B-2
Index
J
JUnit concepts 14
A
abstract class 1
abstraction 1
Acknowledgements 2
action 2
action sequence 2
action state 2
activation 2
activity 7
Activity (from BasicBehaviors) 7
Additional Information 2
align 11
AnyTrigger (from Communications) 8
AssociationClass 11
AssociationEnd 11
Attribute 11
M
ModelElement 11
module ATMTest 14
B
BasicBehaviors 6, 10
behavior 5
Behavior (from BasicBehaviors) 8
BehavioralFeature (from BasicBehaviors, Communications,
specialized) 10
BehavioredClassifier metaclass 5
R
receiver object 6
References 1
C
CallAction 11
Changes to Adopted OMG Specifications 2
Class Descriptions 7
Classifier 11
Common Behavior package 6
Common Behaviors packages 5
communication 6
Communications 10
Communications subpackage 6
concrete syntax 12
Conformance 1
D
DataType 11
Definitions 1
domain model 5
dynamic semantics 5
N
Normative References 1
O
objects 5
Operation 11
Output
Sample Identifier Information File 18
Sample OMG IDL 18
P
Primitive 11
S
Sample Input and Output of WSDL to IDL 17
Scope 1
semantic domain 5
SendAction 11
sending object 6
Signal 11
SimpleTime 7
StructuralFeature 11
Symbols 2
T
Terms and definitions 1
Testing Profile 14
U
UML Metamodel 11
Use of the OCL metamodel in the UML metamodel 12
E
emergent behavior 5
Enumeration 11
EnumLiteral 11
executing behavior 5
F
framework 6
H
How to Read this Specification 2
I
informal explication 5
Input
Sample WSDL 17
Index-1
Index-2

OMG UML2.0 OCL specification

Transcription

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